@article{nokey,

title = {A Hierarchical POD–Neural Network Framework for Data-Driven Inverse Design of Dielectric Elastomer Actuators. Computers and Structures},

author = {Alberto Pérez-Escolar and Jesús Martínez-Frutos and Nathan Ellmer and Antonio J. Gil and Alberto García-González A. and Rogelio Ortigosa},

year  = {2026},

date = {2026-08-10},

journal = {Computers and Structures},

keywords = {},

pubstate = {forthcoming},

tppubtype = {article}

}

@article{Masó2026,

title = {Fully Thermodynamically Consistent and Well-Posed Electro-Thermo-Visco- Hyperelastic Constitutive Framework for Electro-Active Polymers at Finite Strains},

author = {Miguel Masó and Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil and Max Barillas and Alberto García-González and Javier Bonet},

year  = {2026},

date = {2026-07-06},

journal = {Journal of the Mechanics and Physics of Solids},

keywords = {},

pubstate = {forthcoming},

tppubtype = {article}

}

@article{Klein2024b,

title = {Advances in Polyconvex Anisotropic Hyperelasticity},

author = {Dominik Klein and Karl Alexander Kalina and Rogelio Ortigosa and Jesús Martínez-Frutos and Markus Kästner and Oliver Weeger},

editor = {Elsevier},

year  = {2026},

date = {2026-03-15},

urldate = {2026-03-15},

journal = {Journal of the Mechanics and Physics of Solids},

keywords = {},

pubstate = {forthcoming},

tppubtype = {article}

}

@article{Klein2026,

title = {On Limitations of Polyconvexity},

author = {Dominik Klein and Karl Alexander Kalina and Rogelio Ortigosa and Jesús Martínez-Frutos and Markus Kästner and Oliver Weeger},

year  = {2026},

date = {2026-03-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

keywords = {},

pubstate = {forthcoming},

tppubtype = {article}

}

@article{BARILLAS2026116468,

title = {A non-intrusive data-driven approach towards a solution of the inverse problem of bending dielectric elastomer actuators},

author = {Max Barillas and Rogelio Ortigosa and Jesus Martinez-Frutos and Javier Bonet and Alberto García-González},

url = {https://www.sciencedirect.com/science/article/pii/S0307904X25005426},

doi = {https://doi.org/10.1016/j.apm.2025.116468},

issn = {0307-904X},

year  = {2026},

date = {2026-01-01},

urldate = {2026-01-01},

journal = {Applied Mathematical Modelling},

volume = {151},

pages = {116468},

abstract = {Dielectric Elastomer Actuators (DEAs), particularly bending DEAs, have gained significant attention due to their applications in soft robotics, biomimetic systems, and adaptive structures. Recent advancements in computational mechanics and the finite element method (FEM) have enabled accurate simulations of these actuators by incorporating their nonlinear mechanical behavior at large deformations and the coupling between mechanical and electrical responses. However, DEA design often involves solving inverse problems, which become computationally expensive when relying solely on direct simulations. To mitigate this cost, a fast surrogate model is needed. This study proposes a Reduced Order Model (ROM)-based methodology to efficiently determine the optimal locations and magnitudes of applied external potentials in a bending DEA to achieve a desired displacement response. The approach leverages nonlinear dimensionality reduction techniques, specifically Kernel Principal Component Analysis (kPCA) and Isometric Mapping (Isomap), to construct a surrogate model that accurately predicts DEA displacement responses from existing data without modifying the underlying FEM formulation. Using this surrogate model, the inverse problem is solved efficiently, achieving high accuracy (<2 % error) while significantly reducing computational cost. The methodology is validated on two different bending DEA geometries, demonstrating its effectiveness in both surrogate modeling and time-efficient inverse problem solving.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ELLMER2026118349,

title = {Stretch-based hyperelastic electromechanical constitutive metamodels via gradient enhanced Gaussian predictors using hierarchical structure discovery},

author = {Nathan Ellmer and Rogelio Ortigosa and Jesús Martínez-Frutos and Roman Poya and Johann Sienz and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782525006218},

doi = {https://doi.org/10.1016/j.cma.2025.118349},

issn = {0045-7825},

year  = {2026},

date = {2026-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {448},

pages = {118349},

abstract = {This paper introduces a new approach to developing electromechanical constitutive metamodels via the use of Gradient Enhanced Gaussian Predictors (Kriging). The formulation uses principal stretches for the isotropic mechanics, invariants for the electrostatics and coupling terms, and accounts for anisotropy through the relevant inclusion of anisotropic invariants associated with a respective symmetry integrity basis. Three novelties are presented in this paper. The first is the use of orthogonal projections to identify the most appropriate set of inputs - related to material anisotropy - for use in the metamodel. By projecting the stress and electric field data into several derivative bases - defined for each anisotropic class - and then reconstructing the quantities, the errors in reconstruction can be assessed thus inferring the most appropriate class of anisotropy. Furthermore, the procedure forms a pre-processing stage and is particularly useful when an underlying model is completely unknown as seen when modelling Relative Volume Elements. The second novelty arises from the use of a hybrid formulation, namely the principal stretches for isotropic mechanics and the electromechanical anisotropic invariants. This is beneficial during the projection procedure in reducing the cases where the projection matrix becomes singular but requires careful development of the correlation function to maintain physical symmetry conditions. Thirdly, the electromechanical metamodels are calibrated upon the concentric styled data before being integrated within a Finite Element framework and tested upon a range of challenging simulations including bending actuators with induced torsion, frilling due to bending with selected electrode placement, as well as buckling plates tested with three rank-one laminate materials with increasing levels of anisotropy due to physical contrasts. The successful calibration and implementation of the metamodels can be witnessed amongst the wide range of presented numerical examples.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BARILLAS2026108366,

title = {Hyper-reduced order modeling for nonlinear electromechanics using multi-field POD and ECM for dielectric elastomer actuators},

author = {Max Barillas and Rogelio Ortigosa and Jesús Martínez-Frutos and Joaquín A. Hernández and S. Ares Parga and Javier Bonet and Alberto García-González},

url = {https://www.sciencedirect.com/science/article/pii/S0045794926002701},

doi = {https://doi.org/10.1016/j.compstruc.2026.108366},

issn = {0045-7949},

year  = {2026},

date = {2026-01-01},

urldate = {2026-01-01},

journal = {Computers & Structures},

volume = {330},

pages = {108366},

abstract = {This paper introduces a projection-based hyper-reduction methodology within the context of nonlinear electromechanics, specifically tailored for the simulation of dielectric elastomer actuators (DEAs). While high-fidelity finite element (FE) models are robust in capturing complex coupled multiphysics responses (in this case, coupling the quasi-static electric and hyperelastic mechanics responses), their high computational cost often renders them impractical for multi-query engineering problems such as material selection or optimal control. To overcome this limitation, we present a framework that combines a multi-field Proper Orthogonal Decomposition (POD) with the Empirical Cubature Method (ECM). This integration constitutes theone of the first applications of hyper-reduced order modeling (HROM) to handle the high-dimensional nonlinearities inherent in large-deformation electrical-mechanical coupling. A key advantage of this methodology is its ability to preserve the underlying mathematical structure of the high-fidelity FE framework. By treating the assembly of the reduced residual as a quadrature problem, our hyper-reduction scheme ensures that the variational consistency of the original problem is maintained. This guarantees that crucial properties of the tangent stiffness matrix, such as positive or negative definiteness, are inherited by the HROM, which is fundamental to robust and stable Newton–Raphson iterations for strongly nonlinear electromechanical problems. We validate the methodology through complex benchmarks, including a plate beam and a circular membrane geometry. For the most complex cases, the proposed HROM achieved a 35-fold speedup on a standard commercial CPU compared to the full-order model while maintaining a relative error below 1%. This was realized by solving in a reduced space with less than 0.05% of the original dimensionality and evaluating nonlinear operators on a reduced mesh containing less than 20% of the original elements. Finally, the framework is leveraged to perform an exhaustive parametric exploration of material properties for the Ecoflex polymer family under gravitational effects, demonstrating its utility for the accelerated design optimization and material selection in soft robotics.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PATTINSON2025100304,

title = {Towards fully 3D printed dielectric elastomer actuators—A mini review},

author = {Rollo Pattinson and Nathan Ellmer and Mokarram Hossain and Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil and Anil Bastola},

url = {https://www.sciencedirect.com/science/article/pii/S2772369025000374},

doi = {https://doi.org/10.1016/j.addlet.2025.100304},

issn = {2772-3690},

year  = {2025},

date = {2025-01-01},

urldate = {2025-01-01},

journal = {Additive Manufacturing Letters},

volume = {14},

pages = {100304},

abstract = {Dielectric elastomer actuators (DEAs) have attracted the interest of researchers in soft robotics and biomimetics, due to their versatile capabilities, explored through numerical analysis and experimentation. Advances in computational simulation techniques have accelerated numerical studies on DEAs, enabling even design optimisation for improved performance. However, as computational models grow in sophistication, the fabrication methods required often exceed the capabilities of traditional manufacturing. Additive manufacturing, in particular 3D printing, offers a promising solution to the challenges of realising intricate multi-functional designs developed through topology optimisation. Its precision and ability to create complex geometries make it well-suited for translating computational designs into functional DEA devices. This mini-review examines recent progress in 3D printing for DEA fabrication, emphasising its role in bridging the gap between computational design and physical devices. It also highlights emerging technologies and key challenges that must be addressed to fully realise topologically optimised DEA designs.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{perezgarcia2025topology,

title = {Topology and Material Optimization in Ultra-Soft Magneto-Active Structures: Making Advantage of Residual Anisotropies},

author = {Carlos Perez-Garcia and Rogelio Ortigosa and Jesús Martínez-Frutos and Daniel Garcia-Gonzalez},

url = {https://advanced.onlinelibrary.wiley.com/doi/abs/10.1002/adma.202518489},

doi = {10.1002/adma.202518489},

year  = {2025},

date = {2025-01-01},

urldate = {2025-01-01},

journal = {Advanced Materials},

pages = {e18489},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{castanar2025stabilized,

title = {Stabilized Mixed Formulations for Incompressible Finite Strain Electromechanics Including Stress Accurate Analysis},

author = {Inocencio Castañar and Jesús Martínez-Frutos and Rogelio Ortigosa and Ramon Codina},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.70089},

doi = {10.1002/nme.70089},

year  = {2025},

date = {2025-01-01},

urldate = {2025-01-01},

journal = {International Journal for Numerical Methods in Engineering},

volume = {126},

number = {22},

pages = {e70089},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ORTIGOSA2025117741,

title = {A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Alberto Pérez-Escolar and Inocencio Castañar and Nathan Ellmer and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782525000131},

doi = {https://doi.org/10.1016/j.cma.2025.117741},

issn = {0045-7825},

year  = {2025},

date = {2025-01-01},

urldate = {2025-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {437},

pages = {117741},

abstract = {This manuscript introduces a novel neural network-based computational framework for constitutive modeling of thermo-electro-mechanically coupled materials at finite strains, with four key innovations: (i) It supports calibration of neural network models with various input forms, such as Ψnn(F,E0,θ), enn(F,D0,η), Υnn(F,E0,η), or Γnn(F,D0,θ), with F representing the deformation gradient tensor, E0 and D0 the electric field and electric displacement field, respectively and finally, θ and η, the temperature and entropy fields. These models comply with physical laws and material symmetries by utilizing isotropic or anisotropic invariants corresponding to the material’s symmetry group. (ii) A calibration approach is developed for the case of experimental data, where entropy η is typically unmeasurable. (iii) The framework accommodates models like enn(F,D0,η), specially convenient for the imposition of polyconvexity across the three physics involved. A detailed calibration study is conducted evaluating various neural network architectures and considering a large variety of ground truth thermo-electro-mechanical constitutive models. The results demonstrate excellent predictive performance on larger datasets, validated through complex finite element simulations using both ground truth and neural network-based models. Crucially, the framework can be straightforwardly extended to scenarios involving other physics.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{GOMEZSILVA2025107601,

title = {Topology optimization of lattice structures for target band gaps with optimum volume fraction via Bloch-Floquet theory},

author = {Francisco Gómez-Silva and Ramon Zaera and Rogelio Ortigosa and Jesus Martinez-Frutos},

url = {https://www.sciencedirect.com/science/article/pii/S0045794924003304},

doi = {https://doi.org/10.1016/j.compstruc.2024.107601},

issn = {0045-7949},

year  = {2025},

date = {2025-01-01},

urldate = {2025-01-01},

journal = {Computers & Structures},

volume = {307},

pages = {107601},

abstract = {In this work, a topology optimization algorithm has been developed to design bi-material lattice structures showing a band gap around a target frequency, using just one unit cell through the application of Bloch-Floquet theorem. The Bidirectional Evolutionary Structural optimization (BESO) method has been employed, based on bi-material interpolation. A new objective function has been defined, which uses only the natural frequencies closest to the target one, regardless of their position with respect to the fundamental natural frequency. This reduces the computational cost by limiting the number of frequencies considered, and improves the robustness of the optimization process, as these frequencies adapt to changes in the distribution of materials within the domain, constantly encompassing the target frequency. In addition, a novel approach has been implemented to determine the optimal volume fraction of the materials forming the structure, a parameter typically predefined in other works before starting the optimization process. Consequently, the algorithm can autonomously identify the volume that produces the widest band gap around the target frequency. The algorithm has been evaluated for different cases of lattice structures formed by the periodic repetition of a unit cell in both 1D (1D-CR) and 2D (2D-CR), comparing some results with those obtained in other works through different approaches.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ellmer0000,

title = {Stretch-based hyperelastic constitutive emulators through Gradient Enhanced Kriging},

author = {Nathan Ellmer and Rogelio Ortigosa and Jesus Martinez-Frutos and Antonio J. Gil and Roman Poya},

doi = {https://doi.org/10.1016/j.cma.2024.117408},

year  = {2024},

date = {2024-12-01},

urldate = {2024-12-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {423},

abstract = {This paper introduces a new Gradient Enhanced Gaussian Predictor (Kriging) constitutive metamodel based on the use of principal stretches for hyperelasticity. The model further accounts for anisotropy by incorporating suitable invariants of the relevant symmetry integrity basis. The use of stretches is beneficial since it aligns to experimental practices for data gathering, removes the challenge associated with stress projections in isotropy, and increases the range of available constitutive models. This paper presents three significant novelties. The first arises from the proposed approach highlighting the need to enforce physical symmetries and resulted in the authors altering the standard Radial Basis style correlation function to incorporate invariants which naturally uphold these symmetries. The invariants used are both the commonly employed invariants of the right Cauchy–Green strain tensor and the lesser used invariants of the stretch tensor. Note that one may consider using invariants in the correlation function to be the same as using invariants for inputs to the metamodel and this would be true if Ordinary Kriging was used. But the derivatives used in the chain rule clearly result in a new formulation. Secondly, the authors compare two approaches to the infill strategies, one consisting of the error in stress and the other utilising uncertainty provided by Kriging directly. This enables Kriging to guide the user as to most efficient data to insert into the dataset. The final novelty involves the integration of calibrated constitutive metamodels into Finite Element simulations thereby showcasing the accuracy yielded even when handling highly complex deformations such as bending, wrinkling and pinching. Furthermore, the constitutive models are calibrated with data from both isotropic and anisotropic materials such as rank-one laminates, making the accuracy achieved with the small calibration sets even more impressive. The formulation is shown to perform equally well for both synthetic and experimental type of collected data.

},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2024,

title = {Probability-of-failure-based optimization for Random pdes through concentration-of-measure Inequalities},

author = {Rogelio Ortigosa and Jesus Martinez-Frutos and Francisco Periago},

doi = {https://doi.org/10.1051/cocv/2023075},

year  = {2024},

date = {2024-09-23},

urldate = {2024-03-01},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

volume = {30},

number = {66},

abstract = {Control and optimization problems constrained by partial differential equations (PDEs)

with random input data and that incorporate probabilities of failure in their formulations are numerically

extremely challenging, since the computational cost of estimating the tails of a probability

distribution is prohibitive in many situations encountered in real-life engineering problems. In addition,

probabilities of failure are often discontinuous and include huge flat regions where gradients vanish.

Based on the McDiarmid concentration-of-measure inequality, this paper proposes a new functional

which provides a tight and smooth bound for the probability of a given random functional of exceeding

a prescribed threshold parameter. Hence, this approach relieves the above-mentioned difficulties in

the case where the solution map is convex with respect to the random parameter, as in the case of

a deterministic differential operator and the random parameter appearing linearly in the right-hand

side term. Well-posedness of the corresponding optimal control problem is established and the viability

of the proposed method is numerically illustrated by two benchmarks examples arising in topology

optimization and optimal control theory.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa-Martínez2023,

title = {Mathematical modeling, analysis and control in soft robotics: a survey},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

doi = {10.1007/s40324-023-00334-4},

issn = {2281-7875},

year  = {2024},

date = {2024-08-04},

urldate = {2023-08-04},

journal = {SeMA},

publisher = {Springer Science and Business Media LLC},

abstract = {<jats:title>Abstract</jats:title><jats:p>This paper reviews some recent advances in mathematical modeling, analysis and control, both from the theoretical and numerical viewpoints, in the emergent field of soft robotics. The presentation is not focused on specific prototypes of soft robots, but in a more general description of soft smart materials. The goal is to provide a unified and rigorous mathematical approach to open-loop control strategies for soft materials that hopefully might lay the seeds for future research in this field.</jats:p>},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2024b,

title = {Shape-programming in hyperelasticity through differential growth},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

editor = {Springer},

url = {https://link.springer.com/10.1007/s00245-024-10117-6?utm_source=rct_congratemailt&utm_medium=email&utm_campaign=oa_20240323&utm_content=10.1007/s00245-024-10117-6},

doi = {10.1007/s00245-024-10117-6},

issn = {1432-0606},

year  = {2024},

date = {2024-03-23},

urldate = {2024-12-01},

journal = {Applied Mathematics and Optimization},

volume = {89},

number = {49},

abstract = {This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation on a hyperelastic body reaching a given target shape. We consider the two cases of globally compatible growth, where the growth tensor is a deformation gradient over the undeformed domain, and the incompatible one, which discards such hypothesis. We formulate the problem within the framework of optimal control theory in hyperelasticity. The Hausdorff distance is used to quantify dissimilarities between shapes; the complexity of the actuation is incorporated in the cost functional as well. Boundary conditions and external loads are allowed in the state law, thus extending previous works where the stress-free hypothesis turns out to be essential. A rigorous mathematical analysis is then carried out to prove the well-posedness of the problem. The numerical approximation is performed using gradient-based optimisation algorithms. Our main goal in this part is to show the possibility to apply inverse techniques for the numerical approximation of this problem, which allows us to address more generic situations than those covered by analytical approaches. Several numerical experiments for beam-like and shell-type geometries illustrate the performance of the proposed numerical scheme.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Klein2024,

title = {Nonlinear electro-elastic finite element analysis with neural network constitutive models},

author = {Dominik Klein and Rogelio Ortigosa and Jesús Martínez-Frutos and Oliver Weeger},

editor = {Elsevier},

url = {https://www.sciencedirect.com/science/article/pii/S004578252400166X},

doi = {https://doi.org/10.1016/j.cma.2024.116910},

isbn = {1879-2138},

year  = {2024},

date = {2024-03-15},

urldate = {2024-07-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {425},

abstract = {In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material behavior at finite deformations are calibrated to different synthetically generated datasets describing the constitutive response of dielectric elastomers. These include an analytical isotropic potential, a homogenised rank-one laminate, and a homogenised metamaterial with a spherical inclusion. Subsequently, boundary value problems inspired by engineering applications of composite electro-elastic materials are considered. Scenarios with large electrically induced deformations and instabilities are particularly challenging and thus necessitate extensive investigations of the PANN constitutive models in the context of finite element analyses. First of all, an excellent prediction quality of the model is required for very general load cases occurring in the simulation. Furthermore, simulation of large deformations and instabilities poses challenges on the stability of the numerical solver, which is closely related to the constitutive model. In all cases studied, the PANN models yield excellent prediction qualities and a stable numerical behavior even in highly nonlinear scenarios. This can be traced back to the PANN models excellent performance in learning both the first and second derivatives of the ground truth electro-elastic potentials, even though it is only calibrated on the first derivatives. Overall, this work demonstrates the applicability of PANN constitutive models for the efficient and robust simulation of engineering applications of composite electro-elastic materials.

},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Pérez-Escolar2024,

title = {Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors},

author = {Alberto Pérez-Escolar and Jesus Martinez-Frutos and Rogelio Ortigosa and Nathan Ellmer and Antonio J. Gil},

editor = {Springer},

doi = {10.1007/s00466-024-02446-8},

isbn = {1432-0924},

year  = {2024},

date = {2024-02-20},

urldate = {2024-03-01},

journal = {Computational Mechanics},

abstract = {This paper introduces a metamodelling technique that employs gradient-enhanced Gaussian Process Regression (GPR) to emulate diverse internal energy densities based on the deformation gradient tensor F and electric displacement  eld D0. The approach integrates principal invariants as inputs for the surrogate internal energy density, enforcing physical constraints like material frame indi erence and symmetry. This technique enables accurate interpolation of energy and its derivatives, including the  rst Piola-Kirchho  stress tensor and material electric field. The method ensures stress and electric  eld-free conditions at the origin, which is challenging with regression-based methods like neural networks. The paper highlights that using invariants of the dual potential of internal energy density, i.e., the free energy density dependent on the material electric  eld E0, is inappropriate. The saddle point nature of the latter contrasts with the convexity of the internal energy density, creating challenges for GPR or Gradient Enhanced GPR models using invariants of F and E0 (free energy-based GPR), compared to those involving F and D0 (internal energy-based GPR). Numerical examples within a 3D Finite Element framework assess surrogate

model accuracy across challenging scenarios, comparing displacement and stress  elds with ground-truth analytical models. Cases include extreme twisting and electrically induced wrinkles, demonstrating practical applicability and robustness of the proposed approach.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ellmer2024,

title = {Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity},

author = {Nathan Ellmer and Rogelio Ortigosa and Jesus Martinez-Frutos and Antonio J. Gil},

editor = {Elsevier},

doi = {10.1016/j.cma.2023.116547},

isbn = {1879-2138},

year  = {2024},

date = {2024-01-05},

urldate = {2024-01-05},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {418},

issue = {PART B},

pages = {116547},

abstract = {This paper introduces a metamodelling technique that leverages gradient-enhanced Gaussian process regression (also known as gradient-enhanced Kriging), effectively emulating the response of diverse hyperelastic strain energy densities. The approach adopted incorporates principal invariants as inputs for the surrogate of the strain energy density. This integration enables the surrogate to inherently enforce fundamental physical constraints, such as material frame indifference and material symmetry, right from the outset. The proposed approach provides accurate interpolation for energy and the first Piola–Kirchhoff stress tensor (e.g. first order derivatives with respect to inputs). The paper presents three notable innovations. Firstly, it introduces the utilisation of Gradient-Enhanced Kriging to approximate a diverse range of phenomenological models, encompassing numerous isotropic hyperelastic strain energies and a transversely isotropic potential. Secondly, this study marks the inaugural application of this technique for approximating the effective response of composite materials. This includes rank-one laminates, for which analytical solutions are feasible. However, it also encompasses more complex composite materials characterised by a Representative Volume Element (RVE) comprising an elastomeric matrix with a centred spherical inclusion. This extension opens the door for future application of this technique to various RVE types, facilitating efficient three-dimensional computational analyses at the macro-scale of such composite materials, significantly reducing computational time compared to FEM. The third innovation, facilitated by the integration of these surrogate models into a 3D Finite Element computational framework, lies in the assessment of these models scenarios encompassing intricate cases of extreme twisting and more importantly, buckling instabilities in thin-walled structures, thereby highlighting both the practical applicability and robustness of the proposed approach.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa-Martinez2024b,

title = {Mathematical modeling, analysis and control in soft robotics: a survey},

author = {Rogelio Ortigosa-Martínez and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

url = {https://doi.org/10.1007/s40324-023-00334-4},

doi = {10.1007/s40324-023-00334-4},

issn = {2281-7875},

year  = {2024},

date = {2024-01-01},

urldate = {2024-01-01},

journal = {SeMA Journal},

volume = {81},

number = {1},

pages = {147–164},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa-Martinez2024,

title = {Mathematical modeling, analysis and control in soft robotics: a survey},

author = {Rogelio Ortigosa-Martínez and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

url = {https://doi.org/10.1007/s40324-023-00334-4},

doi = {10.1007/s40324-023-00334-4},

issn = {2281-7875},

year  = {2024},

date = {2024-01-01},

journal = {SeMA Journal},

volume = {81},

number = {1},

pages = {147–164},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ORTIGOSA2023346,

title = {Programming shape-morphing electroactive polymers through multi-material topology optimisation},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0307904X23000410},

doi = {https://doi.org/10.1016/j.apm.2023.01.041},

issn = {0307-904X},

year  = {2023},

date = {2023-01-01},

urldate = {2023-01-01},

journal = {Applied Mathematical Modelling},

volume = {118},

pages = {346-369},

abstract = {This paper presents a novel engineering strategy for the design of Dielectric Elastomer (DE) based actuators, capable of attaining complex electrically induced shape morphing configurations. In this approach, a multilayered DE prototype, interleaved with compliant electrodes spreading across the entire faces of the DE, is considered. Careful combination of several DE materials, characterised by different material properties within each of the multiple layers of the device, is pursued. The resulting layout permits the generation of a heterogenous electric field within the device due to the spatial variation of the material properties within the layers and across them. An in-silico or computational approach has been developed in order to facilitate the design of new prototypes capable of displaying predefined electrically induced target configurations. Key features of this framework are: (i) use of a standard two-field Finite Element implementation of the underlying partial differential equations in reversible nonlinear electromechanics, where the unknown fields ot the resulting discrete problem are displacements and the scalar electric potential; (ii) introduction of a novel phase-field driven multi-material topology optimisation framework allowing for the consideration of several DE materials with different material properties, favouring the development of heterogeneous electric fields within the prototype. This novel multi-material framework permits, for the first time, the consideration of an arbitrary number of different N DE materials, by means of the introduction of N−1 phase-field functions, evolving independently over the different layers across the thickness of the device through N−1 Allen-Cahn type evolution equations per layer. A comprehensive series of numerical examples is analysed, with the aim of exploring the capability of the proposed methodology to propose efficient optimal designs. Specifically, the topology optimisation algorithm determines the topology of regions where different DE materials must be conveniently placed in order to attain complex electrically induced configurations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{FRANKE2022114298,

title = {A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics},

author = {M. Franke and Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil and P. Betsch},

url = {https://www.sciencedirect.com/science/article/pii/S0045782521005922},

doi = {https://doi.org/10.1016/j.cma.2021.114298},

issn = {0045-7825},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {389},

pages = {114298},

abstract = {The aim of this paper is the design of a new one-step implicit and thermodynamically consistent Energy–Momentum (EM) preserving time integration scheme for the simulation of thermo-electro-elastic processes undergoing large deformations. The time integration scheme takes advantage of the notion of polyconvexity and of a new tensor cross product algebra. These two ingredients are shown to be crucial for the design of so-called discrete derivatives fundamental for the calculation of the second Piola–Kirchhoff stress tensor, the entropy and the electric field. In particular, the exploitation of polyconvexity and the tensor cross product, enable the derivation of comparatively simple formulas for the discrete derivatives. This is in sharp contrast to much more elaborate discrete derivatives which are one of the main downsides of classical EM time integration schemes. The newly proposed scheme inherits the advantages of EM schemes recently published in the context of thermo-elasticity and electro-mechanics, whilst extending to the more generic case of nonlinear thermo-electro-mechanics. Furthermore, the manuscript delves into suitable convexity/concavity restrictions that thermo-electro-mechanical strain energy functions must comply with in order to yield physically and mathematically admissible solutions. Finally, a series of numerical examples will be presented in order to demonstrate robustness and numerical stability properties of the new EM scheme.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARIN2022114358,

title = {Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers},

author = {Francisco J. Marín and Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782521006319},

doi = {https://doi.org/10.1016/j.cma.2021.114358},

issn = {0045-7825},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {389},

pages = {114358},

abstract = {This paper analyses the viscoelastic up-scaling effects in electro-active polymers endowed with a micro-structure architecture in the form of a rank-one laminate. The principles of rank-n homogenisation and thermodynamical consistency are combined in the context of extremely deformable dielectric elastomers actuated well beyond the onset of geometrical instabilities. To ensure the robustness of the resulting methodology, Convex Multi-Variable (CMV) energy density functionals enriched with a nonlinear continuum viscoelastic description are used to describe the physics of the individual microscopic constituents. The high nonlinearity of the visco-electro-mechanical problem is resolved via a monolithic multi-scale Newton–Raphson scheme with a Backward-Euler (implicit) time integration scheme. A tensor cross product operation between vectors and tensors and an additive decomposition of the micro-scale deformation gradient (in terms of macro-scale and fluctuation components) are used to considerably reduce the complexity of the algebra. The resulting computational framework permits to explore the time-dependent in-silico analysis of rank-one electro-active polymer composites exhibiting extremely complex deformation patterns, paying particular attention to viscoelastic up-scaling effects. A comprehensive series of numerical examples is presented, where specially revealing conclusions about the rate-dependency of the composite electro-active polymer are observed as a function of its microstructure orientation and viscoelastic content. In a rectangular film subjected to extreme bending deformation, two different deformation modes are observed with one prevailing mode depending on the laminate composition. For the case of a square membrane where extreme deformation induces buckling, it is shown that the viscoelastic contribution leads to larger values of (stable) deformation, due to the regularisation that viscoelasticity inherently provides.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ORTIGOSA2022141,

title = {Optimal control and design of magnetic field-responsive smart polymer composites},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0307904X21005096},

doi = {https://doi.org/10.1016/j.apm.2021.10.033},

issn = {0307-904X},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Applied Mathematical Modelling},

volume = {103},

pages = {141-161},

abstract = {This paper presents a novel in-silico framework for the simultaneous optimal control and design of complex magnetic responsive polymer composite materials. State-of-the-art optimisation techniques are used in conjunction with the latest developments in the numerical solution of hard-magnetic soft materials undergoing large (potentially extreme) deformations, in order to address the challenging task of designing shape-morphing two-dimensional composite magnetic sheets. This paper introduces the following key novelties: (i) an optimisation-driven method for the simultaneous optimal control and design of the externally applied magnetic flux density as well as the remnant magnetisation of hard particles within the elastomer matrix, (ii) the well-posedness character of the optimisation problem is established by proving existence of solutions for both the underlying state equation and the control problem itself, (iii) a gradient-based optimisation algorithm is proposed for the numerical approximation of the problem, where explicit expressions of the continuous gradients are obtained by using the formal Lagrangian method. Furthermore, a series of numerical examples are presented in order to demonstrate the capability of the proposal as an alternative to intuition or experimentally-based approaches, representing an optimisation-driven method that facilitates the design of smart materials yielding complex magnetically induced shape morphing configurations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{KLEIN2022115501,

title = {Finite electro-elasticity with physics-augmented neural networks},

author = {Dominik K. Klein and Rogelio Ortigosa and Jesús Martínez-Frutos and Oliver Weeger},

url = {https://www.sciencedirect.com/science/article/pii/S004578252200514X},

doi = {https://doi.org/10.1016/j.cma.2022.115501},

issn = {0045-7825},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {400},

pages = {115501},

abstract = {In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated as a convex neural network. In this way, the model fulfills the polyconvexity condition which ensures material stability, as well as thermodynamic consistency, objectivity, material symmetry, and growth conditions. Depending on the considered invariants, this physics-augmented machine learning model can either be applied for compressible or nearly incompressible material behavior, as well as for arbitrary material symmetry classes. The applicability and versatility of the approach is demonstrated by calibrating it on transversely isotropic data generated with an analytical potential, as well as for the effective constitutive modeling of an analytically homogenized, transversely isotropic rank-one laminate composite and a numerically homogenized cubic metamaterial. These examinations show the excellent generalization properties that physics-augmented neural networks offer also for multi-physical material modeling such as nonlinear electro-elasticity.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ORTIGOSA2022115604,

title = {A computational framework for topology optimisation of flexoelectricity at finite strains considering a multi-field micromorphic approach},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782522005667},

doi = {https://doi.org/10.1016/j.cma.2022.115604},

issn = {0045-7825},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {401},

pages = {115604},

abstract = {This paper presents a novel in-silico framework for the design of flexoelectric energy harvesters at finite strains using topology optimisation. The main ingredients of this work can be summarised as follows: (i) a micromorphic continuum approach is exploited to account for size dependent effects in the context of finite strains, thus permitting the modelling and simulation of flexoelectric effects in highly deformable materials such as dielectric elastomers. A key feature of the multi-field (mixed) formulation pursued is its flexibility as it permits, upon suitable selection of material parameters, to degenerate into other families of high order gradient theories such as flexoelectric gradient elasticity. (ii) A novel energy interpolation scheme is put forward, whereby different interpolation strategies are proposed for the various contributions that the free energy density function is decomposed into. This has enabled to circumvent numerical artifacts associated with fictitious high flexoelectric effects observed in the vicinity of low and intermediate density regions, where extremely high strain gradients tend to develop. (iii) A weighted combination of efficiency-based measures and aggregation functions of the stress is proposed to remedy the shortcomings of state-of-the-art efficiency-based functionals, which promotes the development of hinges with unpractical highly localised large strain gradients. Finally, a series of numerical examples are analysed, studying the development of direct flexoelectricity induced by bending, compression and torsional deformations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortiz-Martínez2021,

title = {Multiplicity of solutions in model-based multiobjective optimization of wastewater treatment plants},

author = {V.M. Ortiz-Martínez, and Jesús Martínez-Frutos and E. Hontoria



},

doi = {https://doi.org/10.1007/s11081-020-09500-3},

year  = {2021},

date = {2021-02-02},

journal = {Optim Eng},

volume = {22},

pages = {1–16},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2021106677,

title = {Robust topology optimization of continuum structures under uncertain partial collapses},

author = {Jesús Martínez-Frutos and Rogelio Ortigosa},

url = {https://www.sciencedirect.com/science/article/pii/S0045794921001991},

doi = {https://doi.org/10.1016/j.compstruc.2021.106677},

issn = {0045-7949},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Computers & Structures},

volume = {257},

pages = {106677},

abstract = {This paper presents a novel probabilistic approach for fail-safe robust topology optimization with the following novelties: (1) the probability for failure to occur at a specified location is considered; (2) the possibility for random failure size is incorporated; (3) a multi-objective problem is pursued encompassing both the expected value of the structural performance and its variance as a robustness criterion. Compared against alternative worst-case-based formulations, the probabilistic framework employed allows designers to assume certain level of risk, avoiding undesirable increments in structural performance due to low probability damage configurations; (4) alternatively to most existing works within fail-safe topology optimization, considering density-based methods, this paper pursues for the first time an optimization technique where the structural boundary is represented implicitly by an iso-level of an optimality criterion field, which is gradually evolved using a bisection method. A key advantage of this technique is that it provides optimized solutions for different volume fractions during the optimization process, allowing to efficiently find a trade-off between structural performance, cost and robustness. Finally, numerical results are included demonstrating the ability of the proposed formulation to provide smooth and clearly defined structural boundaries and to enhance structural robustness with respect to conventional deterministic designs.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARIN2021113567,

title = {A Convex Multi-Variable based computational framework for multilayered electro-active polymers},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Rogelio Ortigosa and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782520307520},

doi = {https://doi.org/10.1016/j.cma.2020.113567},

issn = {0045-7825},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {374},

pages = {113567},

abstract = {This paper presents a novel computational framework for the in silico analysis of rank-one multilayered electro-active polymer composites exhibiting complex deformation patterns. The work applies the principles of rank-n homogenisation in the context of extremely deformable dielectric elastomers actuated beyond the onset of geometrical instabilities. Following previous work by the authors (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016; Ortigosa and Gil, 2016) Convex Multi-Variable (CMV) energy density functionals are used to describe the physics of the individual microscopic constituents, which is shown to guarantee ab initio the existence of solutions for the microstructure problem, described in terms of the so-called deformation gradient and electric displacement amplitude vectors. The high nonlinearity of the quasi-static electro-mechanical problem is resolved via a monolithic multi-scale Newton–Raphson scheme, which is enhanced with a tailor-made arc length technique, used to circumvent the onset of geometrical instabilities. A tensor cross product operation between vectors and tensors and an additive decomposition of the micro-scale deformation gradient (in terms of macro-scale and fluctuation components) are used to considerably reduce the complexity of the algebra. The possible loss of ellipticity of the homogenised constitutive model is strictly monitored through the minors of the homogenised acoustic tensor. A series of numerical examples is presented in order to demonstrate the effect that the volume fraction, the contrast and the material properties, as well as the level of deformation and electric field, have upon the response of the composites when subjected to large three dimensional stretching, bending and torsion, including the possible development of wrinkling.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1137/19M1307299,

title = {Optimal Control of Soft Materials Using a Hausdorff Distance Functional},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

url = {https://doi.org/10.1137/19M1307299},

doi = {10.1137/19M1307299},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {SIAM Journal on Control and Optimization},

volume = {59},

number = {1},

pages = {393-416},

abstract = {This paper addresses, from both theoretical and numerical standpoints, the problem of optimal control of hyperelastic materials characterized by means of polyconvex stored energy functionals. Specifically, inspired by Günnel and Herzog [Front. Appl. Math. Stat., 2 (2016)], a bio-inspired type of external action or control, which resembles the electro-activation mechanism of the human heart, is considered in this paper. The main contribution resides in the consideration of tracking-type cost functionals alternative to those generally used in this field, where the $L^2$ norm of the distance to a given target displacement field is the preferred option. Alternatively, the Hausdorff metric is, for the first time, explored in the context of optimal control in hyperelasticity. The existence of a solution for a regularized version of the optimal control problem is proved. A gradient-based method, which makes use of the concept of shape derivative, is proposed as a numerical resolution method. A series of numerical examples are included illustrating the viability and applicability of the Hausdorff metric in this new context. Furthermore, although not pursued in this paper, it must be emphasized that in contrast to $L^2$ norm tracking-cost functional types, the Hausdorff metric permits the use of potentially very different computational domains for both the target and the actuated soft continuum.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2021104594,

title = {In-silico design of electrode meso-architecture for shape morphing dielectric elastomers},

author = {Jesús Martínez-Frutos and Rogelio Ortigosa and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0022509621002386},

doi = {https://doi.org/10.1016/j.jmps.2021.104594},

issn = {0022-5096},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Journal of the Mechanics and Physics of Solids},

volume = {157},

pages = {104594},

abstract = {This paper presents a novel in-silico tool for the design of complex multilayer Dielectric Elastomers (DEs) characterised by recently introduced layer-by-layer reconfigurable electrode meso-architectures. Inspired by cutting-edge experimental work at Clarke Lab (Harvard) Hajiesmaili and Clarke (2019), this contribution introduces a novel approach underpinned by a diffuse interface treatment of the electrodes, whereby a spatially varying electro-mechanical free energy density is introduced whose active properties are related to the electrode meso-architecture of choice. State-of-the-art phase-field optimisation techniques are used in conjunction with the latest developments in the numerical solution of electrically stimulated DEs undergoing large (potentially extreme) deformations, in order to address the challenging task of finding the most suitable electrode layer-by-layer meso-architecture that results in a specific three-dimensional actuation mode. The paper introduces three key novelties. First, the consideration of the phase-field method for the implicit definition of reconfigurable electrodes placed at user-defined interface regions. Second, the extension of the electrode in-surface phase-field functions to the surrounding dielectric elastomeric volume in order to account for the effect of the presence (or absence) of electrodes within the adjacent elastomeric layers. Moreover, an original energy interpolation scheme of the free energy density is put forward where only the electromechanical contribution is affected by the extended phase-field function, resulting in an equivalent spatially varying active material formulation. Third, consideration of a non-conservative Allen–Cahn type of law for the evolution of the in-surface electrode phase field functions, adapted to the current large strain highly nonlinear electromechanical setting. A series of proof-of-concept examples (in both circular and squared geometries) are presented in order to demonstrate the robustness of the methodology and its potential as a new tool for the design of new DE-inspired soft-robotics components. The ultimate objective is to help thrive the development of this technology through the in-silico production of voltage-tunable (negative and positive Gaussian curvature) DEs shapes beyond those obtained solely via trial-and-error experimental investigation.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2021106677b,

title = {Robust topology optimization of continuum structures under uncertain partial collapses},

author = {Jesús Martínez-Frutos and Rogelio Ortigosa},

url = {https://www.sciencedirect.com/science/article/pii/S0045794921001991},

doi = {https://doi.org/10.1016/j.compstruc.2021.106677},

issn = {0045-7949},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Computers & Structures},

volume = {257},

pages = {106677},

abstract = {This paper presents a novel probabilistic approach for fail-safe robust topology optimization with the following novelties: (1) the probability for failure to occur at a specified location is considered; (2) the possibility for random failure size is incorporated; (3) a multi-objective problem is pursued encompassing both the expected value of the structural performance and its variance as a robustness criterion. Compared against alternative worst-case-based formulations, the probabilistic framework employed allows designers to assume certain level of risk, avoiding undesirable increments in structural performance due to low probability damage configurations; (4) alternatively to most existing works within fail-safe topology optimization, considering density-based methods, this paper pursues for the first time an optimization technique where the structural boundary is represented implicitly by an iso-level of an optimality criterion field, which is gradually evolved using a bisection method. A key advantage of this technique is that it provides optimized solutions for different volume fractions during the optimization process, allowing to efficiently find a trade-off between structural performance, cost and robustness. Finally, numerical results are included demonstrating the ability of the proposed formulation to provide smooth and clearly defined structural boundaries and to enhance structural robustness with respect to conventional deterministic designs.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2021c,

title = {Topology optimisation of stiffeners layout for shape-morphing of dielectric elastomers},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos},

doi = {10.1007/s00158-021-03047-2},

issn = {1615-1488},

journal = {Struct Multidisc Optim},

volume = {64},

number = {6},

pages = {3681--3703},

publisher = {Springer Science and Business Media LLC},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2020888,

title = {Robust optimal control of stochastic hyperelastic materials},

author = {Jesus Martínez-Frutos and Rogelio Ortigosa and Pablo Pedregal and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0307904X20303772},

doi = {https://doi.org/10.1016/j.apm.2020.07.012},

issn = {0307-904X},

year  = {2020},

date = {2020-01-01},

urldate = {2020-01-01},

journal = {Applied Mathematical Modelling},

volume = {88},

pages = {888-904},

abstract = {Soft robots are highly nonlinear systems made of deformable materials such as elastomers, fluids and other soft matter, that often exhibit intrinsic uncertainty in their elastic responses under large strains due to microstructural inhomogeneity. These sources of uncertainty might cause a change in the dynamics of the system leading to a significant degree of complexity in its controllability. This issue poses theoretical and numerical challenges in the emerging field of optimal control of stochastic hyperelasticity. This paper states and solves the robust averaged control in stochastic hyperelasticity where the underlying state system corresponds to the minimization of a stochastic polyconvex strain energy function. Two bio-inspired optimal control problems under material uncertainty are addressed. The expected value of the L2-norm to a given target configuration is minimized to reduce the sensitivity of the spatial configuration to variations in the material parameters. The existence of optimal solutions for the robust averaged control problem is proved. Then the problem is solved numerically by using a gradient-based method. Two numerical experiments illustrate both the performance of the proposed method to ensure the robustness of the system and the significant differences that may occur when uncertainty is incorporated in this type of control problems.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ORTIGOSA2020113395,

title = {A new energy–momentum time integration scheme for non-linear thermo-mechanics},

author = {Rogelio Ortigosa and Antonio J. Gil and Jesus Martínez-Frutos and M. Franke and Javier Bonet},

url = {https://www.sciencedirect.com/science/article/pii/S0045782520305806},

doi = {https://doi.org/10.1016/j.cma.2020.113395},

issn = {0045-7825},

year  = {2020},

date = {2020-01-01},

urldate = {2020-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {372},

pages = {113395},

abstract = {The aim of this paper is the design a new one-step implicit and thermodynamically consistent Energy–Momentum (EM) preserving time integration scheme for the simulation of thermo-elastic processes undergoing large deformations and temperature fields. Following Bonet et al. (2020), we consider well-posed constitutive models for the entire range of deformations and temperature. In that regard, the consideration of polyconvexity inspired constitutive models and a new tensor cross product algebra are shown to be crucial in order to derive the so-called discrete derivatives, fundamental for the construction of the algorithmic derived variables, namely the second Piola–Kirchoff stress tensor and the entropy (or the absolute temperature). The proposed scheme inherits the advantages of the EM scheme recently published by Franke et al. (2018), whilst resulting in a simpler scheme from the implementation standpoint. A series of numerical examples will be presented in order to demonstrate the robustness and applicability of the new EM scheme. Although the examples presented will make use of a temperature-based version of the EM scheme (using the Helmholtz free energy as the thermodynamical potential and the temperature as the thermodynamical state variable), we also include in an Appendix an entropy-based analogue EM scheme (using the internal energy as the thermodynamical potential and the entropy as the thermodynamical state variable).},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2019,

title = {A new stabilisation approach for level-set based topology optimisation of hyperelastic materials},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil



},

doi = {https://doi.org/10.1007/s00158-019-02324-5},

isbn = {1615-147X},

year  = {2019},

date = {2019-02-01},

urldate = {2019-02-01},

journal = {Struct Multidisc Optim},

volume = {60},

pages = {2343–2371},

abstract = {This paper introduces a novel computational approach for level-set based topology optimisation of hyperelastic materials at large strains. This, to date, is considered an unresolved open problem in topology optimisation due to its extremely challenging nature. Two computational strategies have been proposed to address this problem. The first strategy resorts to an arc-length in the pre-buckling region of intermediate topology optimisation (TO) iterations where numerical difficulties arise (associated with nucleation, disconnected elements, etc.), and is then continued by a novel regularisation technique in the post-buckling region. In the second strategy, the regularisation technique is used for the entire loading process at each TO iteration. The success of both rests on the combination of three distinct key ingredients. First, the nonlinear equilibrium equations of motion are solved in a consistent incrementally linearised fashion by splitting the design load into a number of load increments. Second, the resulting linearised tangent elasticity tensor is stabilised (regularised) in order to prevent its loss of positive definiteness and, thus, avoid the loss of convexity of the discrete tangent operator. Third, and with the purpose of avoiding excessive numerical stabilisation, a scalar degradation function is applied on the regularised linearised elasticity tensor, based on a novel regularisation indicator field. The robustness and applicability of this new methodological approach are thoroughly demonstrated through an ample spectrum of challenging numerical examples, ranging from benchmark two-dimensional (plane stress) examples to larger scale three-dimensional applications. Crucially, the performance of all the designs has been tested at a post-processing stage without adding any source of artificial stiffness. Specifically, an arc-length Newton-Raphson method has been employed in conjunction with a ratio of the material parameters for void and solid regions of 10e-12.



},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Baiges2018,

title = {Large-scale stochastic topology optimization using adaptive mesh refinement and coarsening through a two-level parallelization scheme},

author = {Joan Baiges and Jesus Martinez-Frutos and Fermín Otero and Alex Ferrer},

url = {https://www.sciencedirect.com/science/article/pii/S0045782518304237},

doi = {https://doi.org/10.1016/j.cma.2018.08.028},

year  = {2019},

date = {2019-01-01},

urldate = {2019-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {343},

number = {1},

pages = {186-206},

abstract = {Topology optimization under uncertainty of large-scale continuum structures is a computational challenge due to the combination of large finite element models and uncertainty propagation methods. The former aims to address the ever-increasing complexity of more and more realistic models, whereas the latter is required to estimate the statistical metrics of the formulation. In this work, the computational burden of the problem is addressed using a sparse grid stochastic collocation method, to calculate the statistical metrics of the topology optimization under uncertainty formulation, and a parallel adaptive mesh refinement method, to efficiently solve each of the stochastic collocation nodes. A two-level parallel processing scheme (TOUU-PS2) is proposed to profit from parallel computation on distributed memory systems: the stochastic nodes are distributed through the distributed memory system, and the efficient computation of each stochastic node is performed partitioning the problem using a domain decomposition strategy and solving each subdomain using an adaptive mesh refinement method. A dynamic load-balancing strategy is used to balance the workload between subdomains, and thus increasing the parallel performance by reducing processor idle time. The topology optimization problem is addressed using the topological derivative concept in combination with a level-set method. The performance and scalability of the proposed methodology are evaluated using several numerical benchmarks and real-world applications, showing good performance and scalability up to thousands of processors.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2018b,

title = {Structural optimization under internal porosity constraints using topological derivatives},

author = {Jesús Martínez-Frutos and Grégoire Allaire and Charles Dapogny and Francisco Periago},

url = {https://hal.archives-ouvertes.fr/hal-01790472v1 

https://www.sciencedirect.com/science/article/pii/S0045782518305401},

doi = {https://doi.org/10.1016/j.cma.2018.10.036},

year  = {2019},

date = {2019-01-01},

urldate = {2019-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {345},

pages = {1-25},

abstract = {Porosity is a well-known phenomenon occurring during various manufacturing processes (casting, welding, additive manufacturing) of solid structures, which undermines their reliability and mechanical performance. The main purpose of this article is to introduce a new constraint functional of the domain which controls the negative impact of porosity on elastic structures in the framework of shape and topology optimization. The main ingredient of our modeling is the notion of topological derivative, which is used in a slightly unusual way: instead of being an indicator of where to nucleate holes in the course of the optimization process, it is a component of a new constraint functional which assesses the influence of pores on the mechanical performance of structures. The shape derivative of this constraint is calculated and incorporated into a level set based shape optimization algorithm. Our approach is illustrated by several two- and three-dimensional numerical experiments of topology optimization problems constrained by a control on the porosity effect.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Marín2018b,

title = {A polynomial chaos-based approach to risk-averse piezoelectric control of random vibrations of beams},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Francisco Periago},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5823},

issn = {1097-0207},

year  = {2018},

date = {2018-08-10},

urldate = {2018-08-10},

journal = {International Journal for Numerical Methods in Engineering},

volume = {115},

number = {6},

pages = {738-755},

abstract = {This paper proposes a risk-averse formulation for the problem of piezoelectric control of random vibrations of elastic structures. The proposed formulation, inspired by the notion of risk aversion in Economy, is applied to the piezoelectric control of a Bernoulli-Euler beam subjected to uncertainties in its input data. To address the high computational burden associated to the presence of random fields in the model and the discontinuities involved in the cost functional and its gradient, a combination of a non-intrusive anisotropic polynomial chaos approach for uncertainty propagation with a Monte Carlo sampling method is proposed. In a first part, the well-posedness of the control problem is established by proving the existence of optimal controls. In a second part, an adaptive gradient-based method is proposed for the numerical resolution of the problem. Several experiments illustrate the performance of the proposed approach and the significant differences that may occur between the classical deterministic formulation of the problem and its stochastic risk-averse counterpart.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2018,

title = {Evolutionary topology optimization of continuum structures under uncertainty using sensitivity analysis and smooth boundary representation},

author = {Jesús Martínez-Frutos},

url = {https://www.sciencedirect.com/science/article/pii/S0045794917317832},

year  = {2018},

date = {2018-08-01},

urldate = {2018-08-01},

journal = {Computers and Structures},

volume = {205},

pages = {15-27},

abstract = {This paper presents an evolutionary approach for the Robust Topology Optimization (RTO) of continuum structures under loading and material uncertainties. The method is based on an optimality criterion obtained from the stochastic linear elasticity problem in its weak form. The smooth structural topology is determined implicitly by an iso-value of the optimality criterion field. This isovalue is updated using an iterative approach to reach the solution of the RTO problem. The proposal permits to model the uncertainty using random variables with different probability distributions as well as random fields. The computational burden, due to the high dimension of the random field approximation, is efficiently addressed using anisotropic sparse grid stochastic collocation methods. The numerical results show the ability of the proposal to provide smooth and clearly defined structural boundaries. Such results also show that the method provides structural designs satisfying a trade-o between conflicting objectives in the RTO problem.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{JMF_CMAME_2017,

title = {Risk-averse structural topology optimization under random fields using stochastic expansion methods},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0045782517306990 

http://www.upct.es/mc3/files/JMF/riskaverse_cmame.pdf},

issn = {0045-7825},

year  = {2018},

date = {2018-03-01},

urldate = {2018-03-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {330},

pages = {180-206},

abstract = {This work proposes a level-set based approach for solving risk-averse structural topology optimization problems considering random field loading and material uncertainty. The use of random fields increases the dimensionality of the stochastic domain, which poses several computational challenges related to the minimization of the Excess Probability as a measure of risk awareness. This problem is addressed both from the theoretical and numerical viewpoints. First, an existence result under a typical geometrical constraint on the set of admissible shapes is proved. Second, a level-set continuous approach to find the numerical solution of the problem is proposed. Since the considered cost functional has a discontinuous integrand, the numerical approximation of the functional and its sensitivity combine an adaptive anisotropic Polynomial Chaos (PC) approach with a Monte-Carlo (MC) sampling method for uncertainty propagation. Furthermore, to address the increment of dimensionality induced by the random field, an anisotropic sparse grid stochastic collocation method is used for the efficient computation of the PC coefficients. A key point is that the non-intrusive nature of such an approach facilitates the use of High Performance Computing (HPC) to alleviate the computational burden of the problem. Several numerical experiments including random field loading and material uncertainty are presented to show the feasibility of the proposal.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Marín2017,

title = {Robust Averaged Control of Vibrations for the Bernoulli-Euler Beam Equation},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Francisco Periago},

url = {https://doi.org/10.1007/s10957-017-1128-x 

http://localhost/mc3/files/FPE/marin_17.pdf},

doi = {10.1007/s10957-017-1128-x},

issn = {1573-2878},

year  = {2017},

date = {2017-08-01},

urldate = {2017-08-01},

journal = {Journal of Optimization Theory and Applications},

volume = {174},

number = {2},

pages = {428–454},

abstract = {This paper proposes an approach for the robust averaged control of random vibrations for the Bernoulli–Euler beam equation under uncertainty in the flexural stiffness and in the initial conditions. The problem is formulated in the framework of optimal control theory and provides a functional setting, which is so general as to include different types of random variables and second-order random fields as sources of uncertainty. The second-order statistical moment of the random system response at the control time is incorporated in the cost functional as a measure of robustness. The numerical resolution method combines a classical descent method with an adaptive anisotropic stochastic collocation method for the numerical approximation of the statistics of interest. The direct and adjoint stochastic systems are uncoupled, which permits to exploit parallel computing architectures to solve the set of deterministic problem that arise from the stochastic collocation method. As a result, problems with a relative large number of random variables can be solved with a reasonable computational cost. Two numerical experiments illustrate both the performance of the proposed method and the significant differences that may occur when uncertainty is incorporated in this type of control problems.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS201747,

title = {Efficient topology optimization using GPU computing with multilevel granularity},

author = {Jesús Martínez-Frutos},

url = {http://www.sciencedirect.com/science/article/pii/S0965997816302332},

doi = {https://doi.org/10.1016/j.advengsoft.2017.01.009},

issn = {0965-9978},

year  = {2017},

date = {2017-04-01},

urldate = {2017-04-01},

journal = {Advances in Engineering Software},

volume = {106},

number = {Supplement C},

pages = {47 - 62},

abstract = {Abstract This paper proposes a well-suited strategy for High Performance Computing (HPC) of density-based topology optimization using Graphics Processing Units (GPUs). Such a strategy takes advantage of Massively Parallel Processing (MPP) architectures to overcome the computationally demanding procedures of density-based topology design, both in terms of memory consumption and processing time. This is done exploiting data locality and minimizing both memory consumption and data transfers. The proposed GPU instance makes use of different granularities for the topology optimization pipeline, which are selected to properly balance the workload between the threads exploiting the parallelization potential of massively parallel architectures. The performance of the fine-grained GPU instance of the solving stage is evaluated using two preconditioning techniques. The proposal is also compared with the classical CPU implementation for diverse topology optimization problems, including stiffness maximization, heat sink design and compliant mechanism design.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2017119,

title = {GPU acceleration for evolutionary topology optimization of continuum structures using isosurfaces},

author = {Jesús Martínez-Frutos},

url = {http://www.sciencedirect.com/science/article/pii/S004579491630459X},

doi = {https://doi.org/10.1016/j.compstruc.2016.10.018},

issn = {0045-7949},

year  = {2017},

date = {2017-04-01},

urldate = {2017-04-01},

journal = {Computers & Structures},

volume = {182},

number = {Supplement C},

pages = {119 - 136},

abstract = {Abstract Evolutionary topology optimization of three-dimensional continuum structures is a computationally demanding task in terms of memory consumption and processing time. This work aims to alleviate these constraints proposing a well-suited strategy for Graphics Processing Unit (GPU) computing. Such a proposal adopts a fine-grained GPU instance of matrix-free iterative solver for structural analysis and an efficient GPU implementation for isosurface extraction and volume fraction calculation. The performance of the solving stage is evaluated using two preconditioning techniques, including the comparison with the sparse-matrix CPU implementation. The proposal is evaluated using topology optimization problems for real-world applications.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2016393,

title = {Large-scale robust topology optimization using multi-GPU systems},

author = {Jesús Martínez-Frutos},

url = {http://www.sciencedirect.com/science/article/pii/S0045782516309574},

doi = {https://doi.org/10.1016/j.cma.2016.08.016},

issn = {0045-7825},

year  = {2016},

date = {2016-11-01},

urldate = {2016-11-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {311},

number = {Supplement C},

pages = {393 - 414},

abstract = {Abstract Robust topology optimization of continuum structures is an intensive computational task due to the use of uncertainty propagation methods to estimate the statistical metrics within the topology optimization process. Such a computational problem is exacerbated for large finite element (FE) models in terms of memory consumption and processing time. For these reasons, the efficient resolution of robust topology optimization with large models remains an important computational challenge. This work aims to alleviate these computational constraints proposing a well-suited strategy for Graphics Processing Unit (GPU) computing. Such a proposal exploits the multilevel parallelism provided by multi-GPU systems for the parallel execution both within FE models and through uncertainty propagation methods. Task-level parallelism is used to concurrently evaluate the independent simulation models arising from a sparse grid stochastic collocation method. Data-level parallelism with different granularities is then exploited for the efficient resolution of each simulation model and the computation required by the topology optimization process. The resolution of the different calculations of robust topology optimization pipeline using multi-GPU systems are compared to the classically used multi-CPU implementation achieving significant speedups.},

note = {Listed among CMAME’s most downloaded articles from December 2016- February 2017},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NME:NME5210,

title = {Robust optimal Robin boundary control for the transient heat equation with random input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Arnaud Münch and Francisco Periago},

url = {http://dx.doi.org/10.1002/nme.5210 

http://localhost/mc3/files/FPE/ijnme_16.pdf},

doi = {10.1002/nme.5210},

issn = {1097-0207},

year  = {2016},

date = {2016-03-02},

urldate = {2016-03-02},

journal = {International Journal for Numerical Methods in Engineering},

volume = {108},

number = {2},

pages = {116–135},

abstract = {The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient-based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2016271,

title = {Robust shape optimization of continuous structures via the level set method},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {http://www.sciencedirect.com/science/article/pii/S0045782516300834 

http://localhost/mc3/files/FPE/cmame16.pdf},

doi = {https://doi.org/10.1016/j.cma.2016.03.003},

issn = {0045-7825},

year  = {2016},

date = {2016-01-15},

urldate = {2016-01-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {305},

number = {Supplement C},

pages = {271 - 291},

abstract = {Abstract This work proposes a stochastic shape optimization method for continuous structures using the level-set method. Such a method aims to minimize the expected compliance and its variance as measures of the structural robustness. The behavior of continuous structures is modeled by linear elasticity equations with uncertain loading and material. This uncertainty can be modeled using random variables with different probability distributions as well as random fields. The proper problem formulation is ensured by the proof of the existence colorrev of solution under certain geometrical constraints on the set of admissible shapes. The proposed method addresses the stochastic linear elasticity problem in its weak form obtaining the explicit expressions for the continuous shape derivatives. Some numerical examples are presented to show the effectiveness of the proposed approach.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2016,

title = {Kriging-based infill sampling criterion for constraint handling in multi-objective optimization},

author = {Jesús Martínez-Frutos},

url = {https://doi.org/10.1007/s10898-015-0370-8},

doi = {10.1007/s10898-015-0370-8},

issn = {1573-2916},

year  = {2016},

date = {2016-01-01},

urldate = {2016-01-01},

journal = {Journal of Global Optimization},

volume = {64},

number = {1},

pages = {97–115},

abstract = {This paper proposes a novel infill sampling criterion for constraint handling in multi-objective optimization of computationally expensive black-box functions. To reduce the computational burden, Kriging models are used to emulate the objective and constraint functions. The challenge of this multi-objective optimization problem arises from the fact that the epistemic uncertainty of the Kriging models should be taken into account to find Pareto-optimal solutions in the feasible domain. This is done by the proposed sampling criterion combining the Expected HyperVolume Improvement of the front of nondominated solutions and the Probability of Feasibility of new candidates. The proposed criterion is non-intrusive and derivative-free, and it is oriented to: (1) problems in which the computational cost is mainly from the function evaluation rather than optimization, and (2) problems that use complex in-house or commercial software that cannot be modified. The results using the proposed sampling criterion are compared with the results using Multi-Objective Evolutionary Algorithms. These results show that the proposed sampling criterion permits to identify both the feasible domain and an approximation of the Pareto front using a reduced number of computationally expensive simulations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2015,

title = {Robust optimal shape design for an elliptic PDE with uncertainty in its input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

doi = {10.1051/cocv/2014049},

issn = {1262-3377},

year  = {2015},

date = {2015-05-20},

urldate = {2015-05-20},

journal = {ESAIM: COCV},

volume = {21},

number = {4},

pages = {901--923},

publisher = {EDP Sciences},

keywords = {},

pubstate = {published},

tppubtype = {article}

}