@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 = {Constitutive modeling, Electro-active polymers, Homogenization, Nonlinear electro-elasticity, Physics-augmented machine learning},

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{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{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{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{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{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{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}

}

@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 = {19274/PI/14},

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{Ortigosa2018b,

title = {An energy-momentum integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics},

author = {Rogelio Ortigosa and M. Franke and A. Janz and Antonio J. Gil and P. Betsch},

url = {https://www.sciencedirect.com/science/article/pii/S0045782518302007},

doi = {https://doi.org/10.1016/j.cma.2018.04.021},

issn = {0045-7825},

year  = {2018},

date = {2018-09-01},

urldate = {2018-09-01},

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

volume = {339},

pages = {1-35},

abstract = {This paper introduces a new one-step second order accurate energy–momentum (EM) preserving time integrator for reversible electro-elastodynamics. The new scheme is shown to be extremely useful for the long-term simulation of electroactive polymers (EAPs) undergoing massive strains and/or electric fields. The paper presents the following main novelties. (1) The formulation of a new energy–momentumtime integrator scheme in the context of nonlinear electro-elastodynamics. (2) The consideration of well-posed ab initio convex multi-variable constitutive models. (3) Based on the use of alternative mixed variational principles, the paper introduces two different EM time integration strategies (one based on the Helmholtz’s and the other based on the internal energy). (4) The new time integrator relies on the definition of four discrete derivatives of the internal/Helmholtz energies representing the algorithmic counterparts of the work conjugates of the right Cauchy–Green deformation tensor, its co-factor, its determinant and the Lagrangian electric displacement field. (6) Proof of thermodynamic consistency and of second order accuracy with respect to time of the resulting algorithm is included. Finally, a series of numerical examples are included in order to demonstrate the robustness and conservation properties of the proposed scheme, specifically in the case of long-term simulations.},

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 = {19274/PI/14},

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 = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Poya2018,

title = {On a family of numerical models for couple stress based exoelectricity for continua and beams},

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

year  = {2018},

date = {2018-07-01},

urldate = {2018-07-01},

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

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Garcia-Blanco2018,

title = {A polyconvex computational formulation for electro-activation in cardiac mechanics},

author = {Emilio Garcia-Blanco and Rogelio Ortigosa and Antonio J. Gil and C. H. Lee and Javier Bonet},

year  = {2018},

date = {2018-07-01},

urldate = {2018-07-01},

journal = {Biomechanics and Modeling in Mechanobiology},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Morales2017,

title = {Robust Optimal Design of Quantum Electronic Devices},

author = {Ociel Morales and Francisco Periago and José A. Vallejo},

url = {https://www.hindawi.com/journals/mpe/2018/3095257/abs/},

issn = {2331-8422},

year  = {2018},

date = {2018-04-05},

urldate = {2018-04-05},

journal = {Mathematical Problems in Engineering},

volume = {2018},

pages = {10},

abstract = {We consider the optimal design of a sequence of quantum barriers in order to manufacture an electronic device at the nanoscale such that the dependence of its transmission coefficient on the bias voltage is linear. The technique presented here is easily adaptable to other response characteristics. The transmission coefficient is computed using the Wentzel-Kramers-Brillouin (WKB) method, so we can explicitly compute the gradient of the objective function. In contrast with earlier treatments, manufacturing uncertainties are incorporated in the model through random variables and the optimal design problem is formulated in a probabilistic setting. As a measure of robustness, a weighted sum of the expectation and the variance of a least-squares performance metric is considered. Several simulations illustrate the proposed approach.},

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 = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Poya2018b,

title = {A curvilinear high order finite element framework for electro-mechanics: From linearised electro-elasticity to massively deformable dielectric elastomers},

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

url = {https://www.sciencedirect.com/science/article/pii/S0045782517306503},

doi = {https://doi.org/10.1016/j.cma.2017.09.020},

year  = {2018},

date = {2018-02-01},

urldate = {2018-02-01},

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

volume = {329},

pages = {75-117},

abstract = {This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (2016) and Ortigosa and Gil (2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications.},

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 = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Poya2017,

title = {A high performance data parallel tensor contraction framework: Application to coupled electro-mechanics},

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

url = {https://www.sciencedirect.com/science/article/pii/S0010465517300681},

doi = {https://doi.org/10.1016/j.cpc.2017.02.016},

issn = {0010-4655},

year  = {2017},

date = {2017-07-01},

urldate = {2017-07-01},

journal = {Computer Physics Communications},

volume = {216},

pages = {35-52},

abstract = {The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{andAntonioGil2017,

title = {A framework for polyconvex large strain phase-field methods to fracture},

author = {C. Hesch and Antonio J. Gil and Rogelio Ortigosa and M. Dittmann and C. Bilgen and P. Betsch and M. Franke and A. Janz and K.Weinberg},

url = {https://www.sciencedirect.com/science/article/pii/S0045782516309677},

doi = {https://doi.org/10.1016/j.cma.2016.12.035},

issn = {0045-7825},

year  = {2017},

date = {2017-04-15},

urldate = {2017-04-15},

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

volume = {317},

pages = {649-683},

abstract = {Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy–Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn–Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu–Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials.},

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 = {19274/PI/14},

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 = {19274/PI/14},

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 = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016b,

title = {A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies},

author = {Rogelio Ortigosa and Antonio J. Gil and C. H. Lee},

url = {https://www.sciencedirect.com/science/article/pii/S0045782516302286},

doi = {https://doi.org/10.1016/j.cma.2016.06.025},

issn = {0045-7825},

year  = {2016},

date = {2016-10-01},

urldate = {2016-10-01},

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

volume = {310},

pages = {297-334},

abstract = {The series of papers published by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 0000) introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations and/or extreme electric fields. Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Gil and Ortigosa (2016) in the context of compressible electro-elasticity, a novel extended Hu–Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-variable energy functionals. Ultimately, this leads to the definition of new tangent operators for the Helmholtz’s energy functional in the specific context of incompressible electro-elasticity. Fifth, a Petrov–Galerkin stabilisation technique is applied on the three-field formulation for the circumvention of the Ladyz˘enskaja–Babus˘ka–Brezzi (LBB) condition, enabling the use of linear tetrahedral finite elements for the interpolation of the unknowns of the problem. Finally, a series of challenging numerical examples is presented in order to provide an exhaustive comparison of the different variational formulations presented in this paper.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016c,

title = {A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto- mechanics},

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

url = {https://www.sciencedirect.com/science/article/pii/S0045782516303991},

doi = {https://doi.org/10.1016/j.cma.2016.05.019},

issn = {0045-7825},

year  = {2016},

date = {2016-09-01},

urldate = {2016-09-01},

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

volume = {309},

pages = {202-242},

abstract = {This work is the third on a series of papers by Gil and Ortigosa (Gil and Ortigosa 2016; Ortigosa and Gil 2016) on the development of a new computational framework for the analysis of Electro Active Polymers, where the concept of polyconvexity (Ball 1976) is extended to the case of electro-magneto-mechanical energy functionals. Specifically, four key novelties are incorporated in this paper. Firstly, a new set of first order hyperbolic equations is presented in the context of nonlinear electro-magneto-elasticity, including conservation laws for all the fields of the extended set of arguments which determine the convex multi-variable nature of the internal energy. Secondly, the one-to-one and invertible relationship between this extended set and its associated entropy conjugate set enables the definition of a generalised convex entropy function, resulting in the symmetrisation of the system when expressed in terms of the entropy variables. Thirdly, this paper shows that, after careful analysis of the eigenvalue structure of the system, the definition of multi-variable convexity in Gil and Ortigosa (2016) leads to positive definiteness of the electro-magneto-acoustic tensor. Therefore, multi-variable convexity ensures the satisfaction of the Legendre–Hadamard condition, hence showing that the speeds of propagation of acoustic and electro-magnetic waves in the neighbourhood of a stationary point are real. Finally, under a characteristic experimental set-up for electrostrictive dielectric elastomers, a study of the material stability of convex and non-convex multi-variable constitutive models is carried out.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Bonet2016,

title = {On a tensor cross product based formulation of large strain solid mechanics},

author = {Javier Bonet and Antonio J. Gil and Rogelio Ortigosa},

url = {https://www.sciencedirect.com/science/article/pii/S0045782516303991},

doi = {https://doi.org/10.1016/j.ijsolstr.2015.12.030},

issn = {0020-7683},

year  = {2016},

date = {2016-05-01},

urldate = {2016-05-01},

journal = {International Journal of Solids and Structures},

volume = {84},

pages = {49-63},

abstract = {This paper describes in detail the formulation of large strain solid mechanics based on the tensor cross product, originally presented by R. de Boer (1982) and recently re-introduced by Bonet et al. (2015a) and Bonet et al. (2015b). The paper shows how the tensor cross product facilitates the algebra associated with the area and volume maps between reference and final configurations. These maps, together with the fibre map, make up the fundamental kinematic variables in polyconvex elasticity. The algebra proposed leads to novel expressions for the tangent elastic operator which neatly separates material from geometrical dependencies. The paper derives new formulas for the spatial and material stress and their corresponding elasticity tensors. These are applied to the simple case of a Mooney–Rivlin material model. The extension to transversely isotropic material models is also considered.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016d,

title = {A new framework for large strain electromechanics based on convex multi- variable strain energies: variational formulation and material characterisation},

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

url = {https://www.sciencedirect.com/science/article/pii/S0045782515004168},

doi = {https://doi.org/10.1016/j.cma.2015.11.036},

year  = {2016},

date = {2016-04-15},

urldate = {2016-04-15},

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

volume = {302},

pages = {293-328},

abstract = {Following the recent work of Bonet et al. (2015), this paper postulates a new convex multi-variable variational framework for the analysis of Electro Active Polymers (EAPs) in the context of reversible nonlinear electro-elasticity. This extends the concept of polyconvexity (Ball, 1976) to strain energies which depend on non-strain based variables introducing other physical measures such as the electric displacement. Six key novelties are incorporated in this work. First, a new definition of the electro-mechanical internal energy is introduced expressed as a convex multi-variable function of a new extended set of electromechanical arguments. Crucially, this new definition of the internal energy enables the most accepted constitutive inequality, namely ellipticity, to be extended to the entire range of deformations and electric fields and, in addition, to incorporate the electro-mechanical energy of the vacuum, and hence that for ideal dielectric elastomers, as a degenerate case. Second, a new extended set of variables, work conjugate to those characterising the new definition of multi-variable convexity, is introduced in this paper. Third, both new sets of variables enable the definition of novel extended Hu–Washizu type of mixed variational principles which are presented in this paper for the first time in the context of nonlinear electro-elasticity. Fourth, some simple strategies to create appropriate convex multi-variable energy functionals (in terms of convex multi-variable invariants) by incorporating minor modifications to a priori non-convex multi-variable functionals are also presented. Fifth, a tensor cross product operation (de Boer, 1982) used in Bonet et al. (2015) to facilitate the algebra associated with the adjoint of the deformation gradient tensor is incorporated in the proposed variational electro-mechanical framework, leading to insightful representations of otherwise complex algebraic expressions. Finally, under a characteristic experimental setup in dielectric elastomers, the behaviour of a convex multi-variable constitutive model capturing some intrinsic nonlinear effects such as electrostriction, is numerically studied.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016e,

title = {A new framework for large strain electromechanics based on convex multi- variable strain energies: Finite Element discretisation and computational implementation},

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

url = {https://www.sciencedirect.com/science/article/pii/S0045782515004090},

doi = {https://doi.org/10.1016/j.cma.2015.12.007},

issn = {0045-7825},

year  = {2016},

date = {2016-04-15},

urldate = {2016-04-15},

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

volume = {302},

pages = {329-360},

abstract = {In Gil and Ortigosa (2016), Gil and Ortigosa introduced a new convex multi-variable framework for the numerical simulation of Electro Active Polymers (EAPs) in the presence of extreme deformations and electric fields. This extends the concept of polyconvexity to strain energies which depend on non-strain based variables. The consideration of the new concept of multi-variable convexity guarantees the well posedness of generalised Gibbs’ energy density functionals and, hence, opens up the possibility of a new family of mixed variational principles. The aim of this paper is to present, as an example, the Finite Element implementation of two of these mixed variational principles. These types of enhanced methodologies are known to be necessary in scenarios in which the simpler displacement-potential based formulation yields non-physical results, such as volumetric locking, bending and shear locking, pressure oscillations and electro-mechanical locking, to name but a few. Crucially, the use of interpolation spaces in which some of the unknown fields are described as piecewise discontinuous across elements can be used in order to efficiently condense these fields out. This results in mixed formulations with a computational cost comparable to that of the displacement-potential based approach, yet far more accurate. Finally, a series of very challenging numerical examples are presented in order to demonstrate the accuracy, robustness and efficiency of the proposed methodology.},

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 = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Gil2016,

title = {A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity},

author = {Antonio J. Gil and C. H. Lee and Javier Bonet and Rogelio Ortigosa},

url = {https://www.sciencedirect.com/science/article/pii/S0045782515003631},

doi = {https://doi.org/10.1016/j.cma.2015.11.010},

issn = {0045-7825},

year  = {2016},

date = {2016-03-01},

urldate = {2016-03-01},

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

volume = {300},

pages = {146-181},

abstract = {In Part I of this series, Bonet et al. (2015) introduced a new computational framework for the analysis of large strain isothermal fast solid dynamics, where a mixed set of Total Lagrangian conservation laws was presented in terms of the linear momentum and an extended set of strain measures, namely the deformation gradient, its co-factor and its Jacobian. The main aim of this paper is to expand this formulation to the case of nearly incompressible and truly incompressible materials. The paper is further enhanced with three key novelties. First, the use of polyconvex nearly incompressible strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes. Two variants of the same formulation can then be obtained, namely, conservation-based and entropy-based, depending on the unknowns of the system. Crucially, the study of the eigenvalue structure of the system is carried out in order to demonstrate its hyperbolicity and, thus, obtain the correct time step bounds for explicit time integrators. Second, the development of a stabilised Petrov–Galerkin framework is presented for both systems of hyperbolic equations, that is, when expressed in terms of either conservation or entropy variables. Third, an adapted fractional step method, built upon the work presented in Gil et al. (2014), is presented to extend the range of applications towards the incompressibility limit. Finally, a series of numerical examples are presented in order to assess the applicability and robustness of the proposed formulation. The overall scheme shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding equal order of convergence for velocities and stresses.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016f,

title = {A computational framework for polyconvex large strain elasticity for geometrically exact beam theory},

author = {Rogelio Ortigosa and Antonio J. Gil and Javier Bonet and Christian Hesch},

url = {https://link.springer.com/article/10.1007/s00466-015-1231-5},

doi = {https://doi.org/10.1007/s00466-015-1231-5},

issn = {0178-7675},

year  = {2016},

date = {2016-02-01},

urldate = {2016-02-01},

journal = {Computational Mechanics},

volume = {57},

pages = {277–303},

abstract = {In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55–70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney–Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}