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An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics

R. Ortigosa, M. Franke, A. Janz, A.J. Gil, P. Betsch, Antonio Gil Orcid Logo, Rogelio Martinez

Computer Methods in Applied Mechanics and Engineering, Volume: 339, Pages: 1 - 35

Swansea University Authors: Antonio Gil Orcid Logo, Rogelio Martinez

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 fi...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39597
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spelling 2018-06-18T12:00:05.2598843 v2 39597 2018-04-27 An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 80e7ab60860604f60530676f5037d225 Rogelio Martinez Rogelio Martinez true false 2018-04-27 CIVL 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 momentum time 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. Journal Article Computer Methods in Applied Mechanics and Engineering 339 1 35 00457825 Electroactive polymer; Electro-elastodynamics; Multi-variable convexity; Energy–momentum scheme 31 12 2018 2018-12-31 10.1016/j.cma.2018.04.021 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2018-06-18T12:00:05.2598843 2018-04-27T12:50:43.3846282 College of Engineering Engineering R. Ortigosa 1 M. Franke 2 A. Janz 3 A.J. Gil 4 P. Betsch 5 Antonio Gil 0000-0001-7753-1414 6 Rogelio Martinez 7 0039597-30042018114431.pdf ortigosa2018(2).pdf 2018-04-30T11:44:31.3770000 Output 10089823 application/pdf Accepted Manuscript true 2019-04-28T00:00:00.0000000 true eng
title An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics
spellingShingle An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics
Antonio Gil
Rogelio Martinez
title_short An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics
title_full An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics
title_fullStr An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics
title_full_unstemmed An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics
title_sort An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
80e7ab60860604f60530676f5037d225
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
80e7ab60860604f60530676f5037d225_***_Rogelio Martinez
author Antonio Gil
Rogelio Martinez
author2 R. Ortigosa
M. Franke
A. Janz
A.J. Gil
P. Betsch
Antonio Gil
Rogelio Martinez
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 339
container_start_page 1
publishDate 2018
institution Swansea University
issn 00457825
doi_str_mv 10.1016/j.cma.2018.04.021
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
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description 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 momentum time 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.
published_date 2018-12-31T03:53:44Z
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score 10.887713