@article{HORAK2023115695,

title = {A polyconvex transversely-isotropic invariant-based formulation for electro-mechanics: Stability, minimisers and computational implementation},

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

url = {https://www.sciencedirect.com/science/article/pii/S0045782522006508},

doi = {https://doi.org/10.1016/j.cma.2022.115695},

issn = {0045-7825},

year  = {2023},

date = {2023-01-01},

urldate = {2023-01-01},

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

volume = {403},

pages = {115695},

abstract = {The use of Electro-Active Polymers (EAPs) for the fabrication of evermore sophisticated miniaturised soft robotic actuators has seen an impressive development in recent years. The incorporation of crystallographic anisotropic micro-architectures, within an otherwise nearly uniform isotropic soft polymer matrix, has shown great potential in terms of advanced three-dimensional actuation (i.e. stretching, bending, twisting), especially at large strains, that is, beyond the onset of geometrical pull-in instabilities. From the computational point of view, the design of accurate and robust albeit efficient constitutive models is a very active area of research. This paper introduces a novel polyconvex phenomenological invariant-based transversely isotropic formulation (and relevant computational frameworks) for the simulation of transversely isotropic EAPs at large strains, where the ab initio satisfaction of polyconvexity is exploited to ensure the robustness of numerical results for any range of deformations and applied electric fields. The paper also presents key important results both in terms of the existence of minimisers and material stability of coupled electro-mechanics, enhancing previous works in the area of large strain elasticity. In addition, a comprehensive series of selected numerical examples is included in order to demonstrate the effect that the anisotropic orientation and the contrast of material properties, as well as the level of deformation and electric field, have upon the response of the EAP when subjected to large three-dimensional stretching, bending and torsion, including the possible development of wrinkling and the potential loss of ellipticity in ill-posed constitutive models.},

keywords = {Dielectric elastomers, Electro-elasticity, Finite element method, Polyconvexity, Transversely isotropic},

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{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{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}

}