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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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. |
doi_str_mv | 10.1016/j.cma.2021.114358 |
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•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.</description><identifier>ISSN: 0045-7825</identifier><identifier>EISSN: 1879-2138</identifier><identifier>DOI: 10.1016/j.cma.2021.114358</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>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</subject><ispartof>Computer methods in applied mechanics and engineering, 2022-02, Vol.389, p.114358, Article 114358</ispartof><rights>2021 Elsevier B.V.</rights><rights>Copyright Elsevier BV Feb 1, 2022</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-8741e1796575bb93ecc13380d697eb6eedbb39d28df9213733ab5438941e16693</citedby><cites>FETCH-LOGICAL-c325t-8741e1796575bb93ecc13380d697eb6eedbb39d28df9213733ab5438941e16693</cites><orcidid>0000-0001-7753-1414 ; 0000-0002-4542-2237 ; 0000-0002-7112-3345</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0045782521006319$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids></links><search><creatorcontrib>Marín, F.</creatorcontrib><creatorcontrib>Ortigosa, R.</creatorcontrib><creatorcontrib>Martínez-Frutos, J.</creatorcontrib><creatorcontrib>Gil, A.J.</creatorcontrib><title>Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers</title><title>Computer methods in applied mechanics and engineering</title><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.</description><subject>Complexity</subject><subject>Deformation</subject><subject>Deformation effects</subject><subject>Elastomers</subject><subject>Electro-active polymer</subject><subject>Electroactive polymers</subject><subject>Finite element method</subject><subject>Flux density</subject><subject>Formability</subject><subject>Mathematical analysis</subject><subject>Nonlinear electro-elasticity</subject><subject>Nonlinearity</subject><subject>Polymer matrix composites</subject><subject>Rank-one laminates</subject><subject>Regularization</subject><subject>Robustness (mathematics)</subject><subject>Scaling</subject><subject>Tensors</subject><subject>Time dependence</subject><subject>Time integration</subject><subject>Vectors (mathematics)</subject><subject>Viscoelasticity</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-AG8Fz6n5aNMET7L4BQte1IOXkKZTSW2bNeku-O9NrWeHgbk878y8L0KXlOSUUHHd5XYwOSOM5pQWvJRHaEVlpTCjXB6jFSFFiSvJylN0FmNHUknKVuj9zUXroTdxcjbb73C0pnfjRxbM-In9CBm0LdgpZm5MjaPrnfXZ4BvofznfZtAnIHhs7OQOkO18_z1AiOfopDV9hIu_uUav93cvm0e8fX542txuseWsnLCsCgq0UqKsyrpWHKylnEvSCFVBLQCauuaqYbJpVTJTcW7qsuBSzTIhFF-jq2XvLvivPcRJd34fxnRSM8GVUJTwmaILZYOPMUCrd8ENJnxrSvQcoe50ilDPEeolwqS5WTSQ3j84CDpaB6OFxoVkWTfe_aP-AW04eNM</recordid><startdate>20220201</startdate><enddate>20220201</enddate><creator>Marín, F.</creator><creator>Ortigosa, R.</creator><creator>Martínez-Frutos, J.</creator><creator>Gil, A.J.</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-7753-1414</orcidid><orcidid>https://orcid.org/0000-0002-4542-2237</orcidid><orcidid>https://orcid.org/0000-0002-7112-3345</orcidid></search><sort><creationdate>20220201</creationdate><title>Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers</title><author>Marín, F. ; Ortigosa, R. ; Martínez-Frutos, J. ; Gil, A.J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-8741e1796575bb93ecc13380d697eb6eedbb39d28df9213733ab5438941e16693</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Complexity</topic><topic>Deformation</topic><topic>Deformation effects</topic><topic>Elastomers</topic><topic>Electro-active polymer</topic><topic>Electroactive polymers</topic><topic>Finite element method</topic><topic>Flux density</topic><topic>Formability</topic><topic>Mathematical analysis</topic><topic>Nonlinear electro-elasticity</topic><topic>Nonlinearity</topic><topic>Polymer matrix composites</topic><topic>Rank-one laminates</topic><topic>Regularization</topic><topic>Robustness (mathematics)</topic><topic>Scaling</topic><topic>Tensors</topic><topic>Time dependence</topic><topic>Time integration</topic><topic>Vectors (mathematics)</topic><topic>Viscoelasticity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Marín, F.</creatorcontrib><creatorcontrib>Ortigosa, R.</creatorcontrib><creatorcontrib>Martínez-Frutos, J.</creatorcontrib><creatorcontrib>Gil, A.J.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Marín, F.</au><au>Ortigosa, R.</au><au>Martínez-Frutos, J.</au><au>Gil, A.J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2022-02-01</date><risdate>2022</risdate><volume>389</volume><spage>114358</spage><pages>114358-</pages><artnum>114358</artnum><issn>0045-7825</issn><eissn>1879-2138</eissn><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.
•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.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cma.2021.114358</doi><orcidid>https://orcid.org/0000-0001-7753-1414</orcidid><orcidid>https://orcid.org/0000-0002-4542-2237</orcidid><orcidid>https://orcid.org/0000-0002-7112-3345</orcidid></addata></record> |
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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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