More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study

Rubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or ent...

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Main Authors: Hossain Mokarram, Steinmann Paul
Format: Article
Language:English
Published: De Gruyter 2013-06-01
Series:Journal of the Mechanical Behavior of Materials
Subjects:
Online Access:https://doi.org/10.1515/jmbm-2012-0007
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spelling doaj-8be2a65095054f858493cc02fb772dab2021-10-02T17:53:19ZengDe GruyterJournal of the Mechanical Behavior of Materials0334-89382191-02432013-06-01221-2275010.1515/jmbm-2012-0007More hyperelastic models for rubber-like materials: consistent tangent operators and comparative studyHossain Mokarram0Steinmann Paul1Chair of Applied Mechanics, Department of Mechanical Engineering, University of Erlangen-Nuremberg, 5, D-91058, Erlangen, GermanyChair of Applied Mechanics, Department of Mechanical Engineering, University of Erlangen-Nuremberg, 5, D-91058, Erlangen, GermanyRubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.https://doi.org/10.1515/jmbm-2012-0007finite elasticityhyperelasticitymicromechanical modelphenomenological modelrubber-like materialtangent operator
collection DOAJ
language English
format Article
sources DOAJ
author Hossain Mokarram
Steinmann Paul
spellingShingle Hossain Mokarram
Steinmann Paul
More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study
Journal of the Mechanical Behavior of Materials
finite elasticity
hyperelasticity
micromechanical model
phenomenological model
rubber-like material
tangent operator
author_facet Hossain Mokarram
Steinmann Paul
author_sort Hossain Mokarram
title More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study
title_short More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study
title_full More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study
title_fullStr More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study
title_full_unstemmed More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study
title_sort more hyperelastic models for rubber-like materials: consistent tangent operators and comparative study
publisher De Gruyter
series Journal of the Mechanical Behavior of Materials
issn 0334-8938
2191-0243
publishDate 2013-06-01
description Rubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.
topic finite elasticity
hyperelasticity
micromechanical model
phenomenological model
rubber-like material
tangent operator
url https://doi.org/10.1515/jmbm-2012-0007
work_keys_str_mv AT hossainmokarram morehyperelasticmodelsforrubberlikematerialsconsistenttangentoperatorsandcomparativestudy
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