Work - conjugacy of stress and strain tensors and its role in 3D hyperelastic isotropic material formulation

Andreas Dutzler; Werner Guggenberger

doi:10.1002/pamm.202100193

Work - conjugacy of stress and strain tensors and its role in 3D hyperelastic isotropic material formulation

Andreas Dutzler^*, Werner Guggenberger

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In accordance with the framework of hyperelastic isotropic material description it appears possible to replace work-conjugate stress and strain quantities by alternative pairs of work-conjugate stress and strain quantities while other things left unaltered, i.e. based on a retained architecture of the strain energy density function. This replacement results in formally representing different kinds of material response behavior. This may be recognized from the various comparable forms of resulting uniaxial force versus axial stretch behavior in the representative 3D principal axes system. Clarifying and achieving comprehensive understanding of these observations is the main purpose of this paper.

Original language	English
Article number	e202100193
Number of pages	3
Journal	Proceedings in Applied Mathematics and Mechanics
Volume	21
Issue number	1
DOIs	https://doi.org/10.1002/pamm.202100193
Publication status	Published - 14 Dec 2021
Event	91nd Annual Meeting of the International Association of Applied Mathematics and Mechanics: GAMM 2021 - Kassel, Virtuell, Germany Duration: 15 Mar 2021 → 19 Mar 2021 https://jahrestagung.gamm-ev.de/jahr2020-2021/annual-meeting/

Keywords

isotropic hyperelasticity
polar decomposition
work conjugacy

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https://onlinelibrary.wiley.com/doi/epdf/10.1002/pamm.202100193Licence: CC BY 4.0

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title = "Work - conjugacy of stress and strain tensors and its role in 3D hyperelastic isotropic material formulation",

abstract = "In accordance with the framework of hyperelastic isotropic material description it appears possible to replace work-conjugate stress and strain quantities by alternative pairs of work-conjugate stress and strain quantities while other things left unaltered, i.e. based on a retained architecture of the strain energy density function. This replacement results in formally representing different kinds of material response behavior. This may be recognized from the various comparable forms of resulting uniaxial force versus axial stretch behavior in the representative 3D principal axes system. Clarifying and achieving comprehensive understanding of these observations is the main purpose of this paper.",

keywords = "isotropic hyperelasticity, polar decomposition, work conjugacy",

author = "Andreas Dutzler and Werner Guggenberger",

year = "2021",

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doi = "10.1002/pamm.202100193",

language = "English",

volume = "21",

journal = "Proceedings in Applied Mathematics and Mechanics ",

issn = "1617-7061",

publisher = "Wiley-Blackwell",

number = "1",

note = "91nd Annual Meeting of the International Association of Applied Mathematics and Mechanics : GAMM 2021, GAMM 2021 ; Conference date: 15-03-2021 Through 19-03-2021",

url = "https://jahrestagung.gamm-ev.de/jahr2020-2021/annual-meeting/",

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TY - JOUR

T1 - Work - conjugacy of stress and strain tensors and its role in 3D hyperelastic isotropic material formulation

AU - Dutzler, Andreas

AU - Guggenberger, Werner

PY - 2021/12/14

Y1 - 2021/12/14

N2 - In accordance with the framework of hyperelastic isotropic material description it appears possible to replace work-conjugate stress and strain quantities by alternative pairs of work-conjugate stress and strain quantities while other things left unaltered, i.e. based on a retained architecture of the strain energy density function. This replacement results in formally representing different kinds of material response behavior. This may be recognized from the various comparable forms of resulting uniaxial force versus axial stretch behavior in the representative 3D principal axes system. Clarifying and achieving comprehensive understanding of these observations is the main purpose of this paper.

AB - In accordance with the framework of hyperelastic isotropic material description it appears possible to replace work-conjugate stress and strain quantities by alternative pairs of work-conjugate stress and strain quantities while other things left unaltered, i.e. based on a retained architecture of the strain energy density function. This replacement results in formally representing different kinds of material response behavior. This may be recognized from the various comparable forms of resulting uniaxial force versus axial stretch behavior in the representative 3D principal axes system. Clarifying and achieving comprehensive understanding of these observations is the main purpose of this paper.

KW - isotropic hyperelasticity

KW - polar decomposition

KW - work conjugacy

U2 - 10.1002/pamm.202100193

DO - 10.1002/pamm.202100193

M3 - Article

SN - 1617-7061

VL - 21

JO - Proceedings in Applied Mathematics and Mechanics

JF - Proceedings in Applied Mathematics and Mechanics

IS - 1

M1 - e202100193

T2 - 91nd Annual Meeting of the International Association of Applied Mathematics and Mechanics

Y2 - 15 March 2021 through 19 March 2021

ER -

Work - conjugacy of stress and strain tensors and its role in 3D hyperelastic isotropic material formulation

Abstract

Keywords

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