Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers

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 el...

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Veröffentlicht in:Computer methods in applied mechanics and engineering 2022-02, Vol.389, p.114358, Article 114358
Hauptverfasser: Marín, F., Ortigosa, R., Martínez-Frutos, J., Gil, A.J.
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Ortigosa, R.
Martínez-Frutos, J.
Gil, A.J.
description 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. •A computational framework for rank-one multilayered visco-elastic electro-active polymers.•Convex Multi-Variable energy density functions used for microscopic constituents.•Proof of ellipticity of the viscous energetic contribution.•Influence of the laminate orientation on the development of instabilities leading to wrinkling.•Analysis of bending as a function of the laminate orientation through in-silico simulations.
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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. 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subjects Complexity
Deformation
Deformation effects
Elastomers
Electro-active polymer
Electroactive polymers
Finite element method
Flux density
Formability
Mathematical analysis
Nonlinear electro-elasticity
Nonlinearity
Polymer matrix composites
Rank-one laminates
Regularization
Robustness (mathematics)
Scaling
Tensors
Time dependence
Time integration
Vectors (mathematics)
Viscoelasticity
title Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
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