Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity

This paper discusses a new phenomenological continuum formulation for the constitutive modelling of viscoelastic materials at large strains. Following pioneering works in Sidoroff (1974), Lubliner (1985), Bergström (1998) and Reese and Govindjee (1997), the formulation shares some common ingredients...

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Autores: Liu, Zeng, Ortigosa Martínez, Rogelio|||0000-0002-4542-2237, Gil, Antonio J., Bonet Carbonell, Javier|||0000-0002-0430-5181
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/432252
Acceso en línea:https://hdl.handle.net/2117/432252
https://dx.doi.org/10.1016/j.jmps.2025.106194
Access Level:acceso abierto
Palabra clave:Large strain
Finite viscoelasticity
Maxwell rheological model
Multiplicative decomposition
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
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dc.title.none.fl_str_mv Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
title Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
spellingShingle Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
Liu, Zeng
Large strain
Finite viscoelasticity
Maxwell rheological model
Multiplicative decomposition
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
title_short Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
title_full Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
title_fullStr Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
title_full_unstemmed Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
title_sort Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity
dc.creator.none.fl_str_mv Liu, Zeng
Ortigosa Martínez, Rogelio|||0000-0002-4542-2237
Gil, Antonio J.
Bonet Carbonell, Javier|||0000-0002-0430-5181
author Liu, Zeng
author_facet Liu, Zeng
Ortigosa Martínez, Rogelio|||0000-0002-4542-2237
Gil, Antonio J.
Bonet Carbonell, Javier|||0000-0002-0430-5181
author_role author
author2 Ortigosa Martínez, Rogelio|||0000-0002-4542-2237
Gil, Antonio J.
Bonet Carbonell, Javier|||0000-0002-0430-5181
author2_role author
author
author
dc.subject.none.fl_str_mv Large strain
Finite viscoelasticity
Maxwell rheological model
Multiplicative decomposition
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
topic Large strain
Finite viscoelasticity
Maxwell rheological model
Multiplicative decomposition
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
description This paper discusses a new phenomenological continuum formulation for the constitutive modelling of viscoelastic materials at large strains. Following pioneering works in Sidoroff (1974), Lubliner (1985), Bergström (1998) and Reese and Govindjee (1997), the formulation shares some common ingredients with other phenomenological approaches, including the multiplicative decomposition of the deformation gradient into viscous and elastic contributions, the additive Maxwell-type decomposition of the strain energy density, and the definition of a set of kinematic internal state variables with their associated evolution laws. Our formulation departs from other state-of-the-art methodologies via three distinct novelties. First, and revisiting previous work by Bonet (2001), the paper introduces a thermodynamically consistent linear rate type evolution law in terms of stress-type variables, which resembles the return mapping algorithm typically used in elastoplasticity, facilitating the modelling link between both inelastic constitutive models. In this sense, the proposed viscoelastic evolution law can be identified with a classical plastic flow rule. Very importantly, the evolution law is shown to be compatible with the second law of thermodynamics by construction and have a closed-form solution in the case of incompressible viscoelasticity when using a prototypical neo-Hookean type of non-equilibrium strain energy density. Moreover, the paper shows how using the concept of a stress-driven dissipative potential, more general non-linear type of stress evolution laws can be straightforwardly constructed. Second, to facilitate the joint consideration of anisotropy and thermodynamic equilibrium, a frame indifferent stress free configuration is introduced which facilitates the definition of objective strain measures. Third, the methodology is extended from isotropy to transverse isotropy via the consideration of the appropriate structural tensor. The formulation is first displayed for the simple case of a single transversely isotropic invariant contribution with corresponding closed-form solution, and then straightforwardly extended to the consideration of the second transversely isotropic invariant, multiple families of fibres, or even more complex symmetry groups. To demonstrate the capability of the new framework, a specialised form of the eight-chain long-term strain energy (long term) and a neo-Hookean strain energy (non-equilibrium) have been adopted for the description of the mechanical behaviour of VHB 4910 polymer, due to its use in current Electro-Active Polymers based soft robotics. Good agreement is found between in silico predictions and available experimental data on various tests, including loading–unloading cyclic tests, single-step relaxation tests and a multi-step relaxation test. Finally, biaxial loading–unloading cyclic and relaxation tests are presented to further showcase performance in anisotropic scenarios.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-10-01
2025
2025-06-18
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/432252
https://dx.doi.org/10.1016/j.jmps.2025.106194
url https://hdl.handle.net/2117/432252
https://dx.doi.org/10.1016/j.jmps.2025.106194
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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Attribution-NonCommercial-NoDerivatives 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
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spelling Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticityLiu, ZengOrtigosa Martínez, Rogelio|||0000-0002-4542-2237Gil, Antonio J.Bonet Carbonell, Javier|||0000-0002-0430-5181Large strainFinite viscoelasticityMaxwell rheological modelMultiplicative decompositionÀrees temàtiques de la UPC::Enginyeria civil::Materials i estructuresThis paper discusses a new phenomenological continuum formulation for the constitutive modelling of viscoelastic materials at large strains. Following pioneering works in Sidoroff (1974), Lubliner (1985), Bergström (1998) and Reese and Govindjee (1997), the formulation shares some common ingredients with other phenomenological approaches, including the multiplicative decomposition of the deformation gradient into viscous and elastic contributions, the additive Maxwell-type decomposition of the strain energy density, and the definition of a set of kinematic internal state variables with their associated evolution laws. Our formulation departs from other state-of-the-art methodologies via three distinct novelties. First, and revisiting previous work by Bonet (2001), the paper introduces a thermodynamically consistent linear rate type evolution law in terms of stress-type variables, which resembles the return mapping algorithm typically used in elastoplasticity, facilitating the modelling link between both inelastic constitutive models. In this sense, the proposed viscoelastic evolution law can be identified with a classical plastic flow rule. Very importantly, the evolution law is shown to be compatible with the second law of thermodynamics by construction and have a closed-form solution in the case of incompressible viscoelasticity when using a prototypical neo-Hookean type of non-equilibrium strain energy density. Moreover, the paper shows how using the concept of a stress-driven dissipative potential, more general non-linear type of stress evolution laws can be straightforwardly constructed. Second, to facilitate the joint consideration of anisotropy and thermodynamic equilibrium, a frame indifferent stress free configuration is introduced which facilitates the definition of objective strain measures. Third, the methodology is extended from isotropy to transverse isotropy via the consideration of the appropriate structural tensor. The formulation is first displayed for the simple case of a single transversely isotropic invariant contribution with corresponding closed-form solution, and then straightforwardly extended to the consideration of the second transversely isotropic invariant, multiple families of fibres, or even more complex symmetry groups. To demonstrate the capability of the new framework, a specialised form of the eight-chain long-term strain energy (long term) and a neo-Hookean strain energy (non-equilibrium) have been adopted for the description of the mechanical behaviour of VHB 4910 polymer, due to its use in current Electro-Active Polymers based soft robotics. Good agreement is found between in silico predictions and available experimental data on various tests, including loading–unloading cyclic tests, single-step relaxation tests and a multi-step relaxation test. Finally, biaxial loading–unloading cyclic and relaxation tests are presented to further showcase performance in anisotropic scenarios.The authors acknowledge funding received from grants PID2022-141957OB-C21 and PID2022-141957OA-C22 financed by MCIN/AEI /10.13039/501100011033/ FEDER, UE. R. Ortigosa also acknowledges the support provided by the Autonomous Community of the Region of Murcia, Spain, through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundación Séneca - Agencia de Ciencia y Tecnología de la Región de Murcia. A. J. Gil wishes to acknowledge the support provided by the Defence, Science and Technology Laboratory (Dstl) and The Leverhulme Trust Foundation (UK) through a Leverhulme Fellowship. The authors also acknowledge the useful discussions with colleagues Alberto García González and Max Barillas Velásquez from UPC-CIMNE, Jesús Martínez Frutos from Technical University of Cartagena, and graphical support by Nathan Ellmer from Swansea University.20252025-10-0120252025-06-18journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/432252https://dx.doi.org/10.1016/j.jmps.2025.106194reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4322522026-05-27T15:37:01Z
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