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19274/PI/14 21996/PI/22 Analysis Applied Mathematics Computational Mathematics Computational Mechanics Computer Graphics and Computer-Aided Design Computer Science Applications Control and Optimization Control and Systems Engineering DICOPMA Dielectric elastomer Dielectric elastomers Electro-active polymer Energy–momentum scheme Evolutionary topology optimization Fail-safe design Finite element method General Engineering General Mathematics Mechanical Engineering Nonlinear electro-elasticity Numerical Analysis Ocean Engineering Phase-field PID2022-141957OA-C22 Polyconvexity Rank-one laminates Software Topology optimisation 
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2022
 Ortigosa, Rogelio;  Martínez-Frutos, Jesús;  Gil, Antonio J.
A computational framework for topology optimisation of flexoelectricity at finite strains considering a multi-field micromorphic approach Journal Article 
In: Computer Methods in Applied Mechanics and Engineering, vol. 401, pp. 115604, 2022, ISSN: 0045-7825.
Abstract | BibTeX | Tags: DICOPMA, Dielectric elastomer, Energy harvesters, Flexoelectricity, Micromorphic elasticity, Mixed finite elements, Topology optimisation | Links: 
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@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}

}

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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.
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