A thermomechanical framework for constitutive models for rate-independent dissipative materials

A formulation of elastic-plastic theory for rate independent materials is described, based on the use of thermodynamic potentials. The four energy functions commonly used in thermodynamics (internal energy, Helmholtz free energy, enthalpy and Gibbs free energy) are used to provide descriptions depen...

תיאור מלא

מידע ביבליוגרפי
Main Authors: Houlsby, G, Puzrin, A
פורמט: Journal article
שפה:English
יצא לאור: Elsevier 2000
_version_ 1826262759519551488
author Houlsby, G
Puzrin, A
author_facet Houlsby, G
Puzrin, A
author_sort Houlsby, G
collection OXFORD
description A formulation of elastic-plastic theory for rate independent materials is described, based on the use of thermodynamic potentials. The four energy functions commonly used in thermodynamics (internal energy, Helmholtz free energy, enthalpy and Gibbs free energy) are used to provide descriptions depending on which combinations of the stress, strain, temperature and entropy are taken as the independent variables. Much use is made of Legendre transformations to establish the links between the different energy functions. Dissipative behaviour is introduced through the use of kinematic internal parameters, and their conjugate variables, which are termed generalized stresses. A dissipation function or a yield function is used to describe the irreversible behaviour, and these are related by a degenerate case of the Legendre transformation. A central theme is that the constitutive behaviour is entirely determined by the knowledge of two scalar potentials. A systematic presentation is made of 16 possible ways of formulating constitutive behaviour within this framework. From four of these forms it is possible to establish the incremental response entirely by differentiation of the two potentials and by standard matrix manipulation. Examples are provided of the forms of the potentials for certain simple cases. The paper builds on previous work by Ziegler and other authors, and extends and generalizes work by Collins and Houlsby to include thermal effects.
first_indexed 2024-03-06T19:41:10Z
format Journal article
id oxford-uuid:20b33abf-788c-4310-a063-22d9e5f49aab
institution University of Oxford
language English
last_indexed 2024-03-06T19:41:10Z
publishDate 2000
publisher Elsevier
record_format dspace
spelling oxford-uuid:20b33abf-788c-4310-a063-22d9e5f49aab2022-03-26T11:29:05ZA thermomechanical framework for constitutive models for rate-independent dissipative materialsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:20b33abf-788c-4310-a063-22d9e5f49aabEnglishSymplectic Elements at OxfordElsevier2000Houlsby, GPuzrin, AA formulation of elastic-plastic theory for rate independent materials is described, based on the use of thermodynamic potentials. The four energy functions commonly used in thermodynamics (internal energy, Helmholtz free energy, enthalpy and Gibbs free energy) are used to provide descriptions depending on which combinations of the stress, strain, temperature and entropy are taken as the independent variables. Much use is made of Legendre transformations to establish the links between the different energy functions. Dissipative behaviour is introduced through the use of kinematic internal parameters, and their conjugate variables, which are termed generalized stresses. A dissipation function or a yield function is used to describe the irreversible behaviour, and these are related by a degenerate case of the Legendre transformation. A central theme is that the constitutive behaviour is entirely determined by the knowledge of two scalar potentials. A systematic presentation is made of 16 possible ways of formulating constitutive behaviour within this framework. From four of these forms it is possible to establish the incremental response entirely by differentiation of the two potentials and by standard matrix manipulation. Examples are provided of the forms of the potentials for certain simple cases. The paper builds on previous work by Ziegler and other authors, and extends and generalizes work by Collins and Houlsby to include thermal effects.
spellingShingle Houlsby, G
Puzrin, A
A thermomechanical framework for constitutive models for rate-independent dissipative materials
title A thermomechanical framework for constitutive models for rate-independent dissipative materials
title_full A thermomechanical framework for constitutive models for rate-independent dissipative materials
title_fullStr A thermomechanical framework for constitutive models for rate-independent dissipative materials
title_full_unstemmed A thermomechanical framework for constitutive models for rate-independent dissipative materials
title_short A thermomechanical framework for constitutive models for rate-independent dissipative materials
title_sort thermomechanical framework for constitutive models for rate independent dissipative materials
work_keys_str_mv AT houlsbyg athermomechanicalframeworkforconstitutivemodelsforrateindependentdissipativematerials
AT puzrina athermomechanicalframeworkforconstitutivemodelsforrateindependentdissipativematerials
AT houlsbyg thermomechanicalframeworkforconstitutivemodelsforrateindependentdissipativematerials
AT puzrina thermomechanicalframeworkforconstitutivemodelsforrateindependentdissipativematerials