@article{Poya2023b,

title = {Variational schemes and mixed finite elements for large strain isotropic elasticity in principal stretches: Closed‐form tangent eigensystems, convexity conditions, and stabilised elasticity},

author = {Roman Poya and Rogelio Ortigosa and Antonio J. Gil},

doi = {10.1002/nme.7254},

issn = {1097-0207},

year  = {2023},

date = {2023-08-30},

urldate = {2023-08-30},

journal = {Numerical Meth Engineering},

volume = {124},

number = {16},

pages = {3436--3493},

publisher = {Wiley},

abstract = {<jats:title>Abstract</jats:title><jats:p>A new computational framework for large strain elasticity in principal stretches is presented. Distinct from existing literature, the proposed formulation makes direct use of principal stretches rather than their squares that is, eigenvalues of Cauchy‐Green strain tensor. The proposed framework has three key features. First, the eigen‐decomposition of the tangent elasticity and initial (geometric) stiffness operators is obtained in closed‐form from principal information alone. Crucially, these newly found eigenvalues describe the general convexity conditions of isotropic hyperelastic energies. In other words, convexity is postulated concisely through tangent eigenvalues supplementing the original work of Ball (<jats:italic>Arch Ration Mech Anal</jats:italic>. 1976; 63(4): 337–403). Consequently, this novel finding opens the door for designing efficient automated Newton‐style algorithms with stabilised tangents via <jats:italic>closed‐form</jats:italic> semipositive definite projection or spectral shifting that converge irrespective of mesh resolution, quality, loading scenario and without relying on path‐following techniques. A critical study of closed‐form tangent stabilisation in the context of isotropic hyperelasticity is therefore undertaken in this work. Second, in addition to high order displacement‐based formulation, mixed Hu‐Washizu variational principles are formulated in terms of principal stretches by introducing stretch work conjugate Lagrange multipliers that enforce principal stretch‐stress compatibility. This is similar to enhanced strain methods. However, the resulting mixed finite element scheme is cost‐efficient, specially compared to approximating the entire strain tensors since the formulation is in the scalar space of singular values. Third, the proposed framework facilitates simulating rigid and stiff systems and those that are nearly‐inextensible in principal directions, a constituent of elasticity that cannot be easily studied using standard formulations.</jats:p>},

keywords = {Applied Mathematics, DICOPMA, General Engineering, Numerical Analysis},

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  = {2023},

date = {2023-08-04},

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 = {Applied Mathematics, Control and Optimization, DICOPMA, Modeling and Simulation, Numerical Analysis},

pubstate = {published},

tppubtype = {article}

}

@article{Franke2023,

title = {A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics},

author = {M. Franke and Felix Zähringer and Moritz Hille and Rogelio Ortigosa and P. Betsch and Antonio J. Gil},

doi = {10.1002/nme.7209},

issn = {1097-0207},

year  = {2023},

date = {2023-05-30},

urldate = {2023-05-30},

journal = {Numerical Meth Engineering},

volume = {124},

number = {10},

pages = {2135--2170},

publisher = {Wiley},

abstract = {<jats:title>Abstract</jats:title><jats:p>A novel mixed framework and energy‐momentum consistent integration scheme in the field of coupled nonlinear thermo‐electro‐elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of polyconvex strain energy functions. For this elastodynamic framework, the properties of the so‐called tensor cross product are exploited to derive a mixed formulation via a Hu‐Washizu type extension of the strain energy function. Afterwards, a general path to incorporate nonpotential problems for mixed formulations is demonstrated. To this end, the strong form of the mixed framework is derived and supplemented with the energy balance as well as Maxwell's equations neglecting magnetic and time dependent effects. By additionally choosing an appropriate energy function, this procedure leads to a fully coupled thermo‐electro‐elastodynamic formulation which benefits from the properties of the underlying mixed framework. In addition, the proposed mixed framework facilitates the design of a new energy‐momentum consistent time integration scheme by employing discrete derivatives in the sense of Gonzalez. A one‐step integration scheme of second‐order accuracy is obtained which is shown to be stable even for large time steps. Eventually, the performance of the novel formulation is demonstrated in several numerical examples.</jats:p>},

keywords = {Applied Mathematics, DICOPMA, General Engineering, Numerical Analysis},

pubstate = {published},

tppubtype = {article}

}

@article{Remigio-Reyes2022,

title = {Topology optimization-driven design of added rib architecture system for enhanced free vibration response of thin-wall plastic components used in the automotive industry},

author = {Joel Omar Remigio-Reyes and Isaías E. Garduño and José Manuel Rojas-García and Hugo Arcos-Gutiérrez and Rogelio Ortigosa},

doi = {10.1007/s00170-022-10219-x},

issn = {1433-3015},

year  = {2022},

date = {2022-11-00},

urldate = {2022-11-00},

journal = {Int J Adv Manuf Technol},

volume = {123},

number = {3-4},

pages = {1231--1247},

publisher = {Springer Science and Business Media LLC},

keywords = {Computer Science Applications, Control and Systems Engineering, DICOPMA, Industrial and Manufacturing Engineering, Mechanical Engineering, Software},

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 = {DICOPMA, Dielectric elastomers, Electro active polymers, Energy–momentum scheme, Finite element method, Nonlinear thermo-electro-elastodynamics, Polyconvexity, Tensor cross product},

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 = {DICOPMA, Electro-active polymer, Finite element method, Nonlinear electro-elasticity, Rank-one laminates, Viscoelasticity},

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 = {DICOPMA, Hard-magnetic soft materials, Magneto-elasticity, Optimal control, Optimal design, Polyconvexity, Shape-morphing},

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 = {DICOPMA, Dielectric elastomer, Energy harvesters, Flexoelectricity, Micromorphic elasticity, Mixed finite elements, Topology optimisation},

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},

year  = {2021},

date = {2021-12-00},

urldate = {2021-12-00},

journal = {Struct Multidisc Optim},

volume = {64},

number = {6},

pages = {3681--3703},

publisher = {Springer Science and Business Media LLC},

keywords = {Computer Graphics and Computer-Aided Design, Computer Science Applications, Control and Optimization, Control and Systems Engineering, DICOPMA, Software},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2021,

title = {Risk-averse approach for topology optimization of fail-safe structures using the level-set method},

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

doi = {10.1007/s00466-021-02058-6},

issn = {1432-0924},

year  = {2021},

date = {2021-11-00},

urldate = {2021-11-00},

journal = {Comput Mech},

volume = {68},

number = {5},

pages = {1039--1061},

publisher = {Springer Science and Business Media LLC},

keywords = {Applied Mathematics, Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics, DICOPMA, Mechanical Engineering, Ocean Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2021b,

title = {Multi-resolution methods for the topology optimization of nonlinear electro-active polymers at large strains},

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

doi = {10.1007/s00466-021-02030-4},

issn = {1432-0924},

year  = {2021},

date = {2021-08-00},

urldate = {2021-08-00},

journal = {Comput Mech},

volume = {68},

number = {2},

pages = {271--293},

publisher = {Springer Science and Business Media LLC},

keywords = {Applied Mathematics, Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics, DICOPMA, Mechanical Engineering, Ocean Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2021,

title = {Density-based topology optimisation considering nonlinear electromechanics},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and David Ruiz and Alberto Donoso and Jose C. Bellido},

doi = {10.1007/s00158-021-02886-3},

issn = {1615-1488},

year  = {2021},

date = {2021-07-00},

urldate = {2021-07-00},

journal = {Struct Multidisc Optim},

volume = {64},

number = {1},

pages = {257--280},

publisher = {Springer Science and Business Media LLC},

keywords = {Computer Graphics and Computer-Aided Design, Computer Science Applications, Control and Optimization, Control and Systems Engineering, DICOPMA, Software},

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 = {DICOPMA, Dielectric elastomer, Electrode meso-architecture, Phase-field, Shape morphing, Topology optimisation},

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 = {DICOPMA, Evolutionary topology optimization, Fail-safe design, Optimality criterion, Robust design, Structural redundancy},

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 = {Composite materials, DICOPMA, Finite element method, Nonlinear electro-elasticity, Rank-one laminates},

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 = {DICOPMA, Evolutionary topology optimization, Fail-safe design, Optimality criterion, Robust design, Structural redundancy},

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 = {DICOPMA},

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 = {Active fibers, DICOPMA, Hyperelasticity, Material uncertainty, Robust optimal control, Soft robotics, Turgor pressure},

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 = {DICOPMA, Energy–momentum scheme, Finite element method, Nonlinear thermo-elastodynamics, Structure-preserving discretisation},

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 = {DICOPMA},

pubstate = {published},

tppubtype = {article}

}