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A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics

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

Computer Methods in Applied Mechanics and Engineering

Swansea University Author: Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.cma.2019.03.036

Abstract

In Ortigosa et al. (2018), the authors presented a new family of time integrators for large deformation electromechanics. In that paper, definition of appropriate algorithmic expressions for the discrete derivatives of the internal energy and consideration of multi-variable convexity of the internal...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa49620
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spelling 2019-04-11T15:08:15.2404433 v2 49620 2019-03-19 A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2019-03-19 CIVL In Ortigosa et al. (2018), the authors presented a new family of time integrators for large deformation electromechanics. In that paper, definition of appropriate algorithmic expressions for the discrete derivatives of the internal energy and consideration of multi-variable convexity of the internal energy was made. These two ingredients were essential for the definition of a new energy-momentum (EM) time integrator in the context of large deformation electromechanics relying on materially stable (ellipticity compliant) constitutive models. In Betsch et al. (2018), the authors introduced a family of EM time integrators making use of mixed variational principles for large strain mechanics. In addition to the displacement field, the right Cauchy–Green deformation tensor, its co-factor and its Jacobian were introduced as unknown fields in the formulation. An elegant cascade system of kinematic constraints was introduced in this paper, crucial for the satisfaction of the required conservation properties of the new family of EM time integrators. The objective of the present paper is the introduction of new mixed variational principles for EM time integrators in electromechanics, hence bridging the gap between the previous work presented by the authors in References Ortigosa et al. (2018) and Betsch et al. (2018), opening up the possibility to a variety of new Finite Element implementations. The following characteristics of the proposed EM time integrator make it very appealing: (i) the new family of time integrators can be shown to be thermodynamically consistent and second order accurate; (ii) piecewise discontinuous interpolation of the unknown fields (except displacements and electric potential) has been carried out, in order to yield a computational cost comparable to that of standard displacement-potential formulations. 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 0045-7825 Mixed variational framework, Electroactive polymer, Electro-elastodynamics, Multi-variable convexity, energy-momentum scheme 31 12 2019 2019-12-31 10.1016/j.cma.2019.03.036 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2019-04-11T15:08:15.2404433 2019-03-19T11:44:29.8586371 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering M. Franke 1 R. Ortigosa 2 A. Janz 3 A.J. Gil 4 P. Betsch 5 Antonio Gil 0000-0001-7753-1414 6 0049620-19032019114631.pdf franke2019.pdf 2019-03-19T11:46:31.6600000 Output 7782680 application/pdf Accepted Manuscript true 2020-04-01T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng
title A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics
spellingShingle A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics
Antonio Gil
title_short A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics
title_full A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics
title_fullStr A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics
title_full_unstemmed A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics
title_sort A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Antonio Gil
author2 M. Franke
R. Ortigosa
A. Janz
A.J. Gil
P. Betsch
Antonio Gil
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
publishDate 2019
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2019.03.036
college_str Faculty of Science and Engineering
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
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description In Ortigosa et al. (2018), the authors presented a new family of time integrators for large deformation electromechanics. In that paper, definition of appropriate algorithmic expressions for the discrete derivatives of the internal energy and consideration of multi-variable convexity of the internal energy was made. These two ingredients were essential for the definition of a new energy-momentum (EM) time integrator in the context of large deformation electromechanics relying on materially stable (ellipticity compliant) constitutive models. In Betsch et al. (2018), the authors introduced a family of EM time integrators making use of mixed variational principles for large strain mechanics. In addition to the displacement field, the right Cauchy–Green deformation tensor, its co-factor and its Jacobian were introduced as unknown fields in the formulation. An elegant cascade system of kinematic constraints was introduced in this paper, crucial for the satisfaction of the required conservation properties of the new family of EM time integrators. The objective of the present paper is the introduction of new mixed variational principles for EM time integrators in electromechanics, hence bridging the gap between the previous work presented by the authors in References Ortigosa et al. (2018) and Betsch et al. (2018), opening up the possibility to a variety of new Finite Element implementations. The following characteristics of the proposed EM time integrator make it very appealing: (i) the new family of time integrators can be shown to be thermodynamically consistent and second order accurate; (ii) piecewise discontinuous interpolation of the unknown fields (except displacements and electric potential) has been carried out, in order to yield a computational cost comparable to that of standard displacement-potential formulations. 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 2019-12-31T04:00:46Z
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