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On constitutive and configurational aspects of models for gradient continua with microstructure

Svendsen, Bob; Neff, Patrizio and Menzel, Andreas LU (2009) Annual GAMM Meeting 2007 In ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 89(8). p.687-697
Abstract
The purpose of this work is the investigation of some constitutive and configurational aspects of phenomenological model formulations for a class of materials with history-dependent gradient microstructure. The assumption that the behavior of a material point is affected by history-dependent processes in a finite neighbor of this point yields an extended continuum characterized by non-simple material behavior and by additional degrees-of-freedom. This includes both standard micromorphic materials as well as inelastic gradient materials as special cases. As in the case of simple materials, the corresponding constitutive relations are subject to restrictions imposed by material frame-indifference and material symmetry. In the latter case,... (More)
The purpose of this work is the investigation of some constitutive and configurational aspects of phenomenological model formulations for a class of materials with history-dependent gradient microstructure. The assumption that the behavior of a material point is affected by history-dependent processes in a finite neighbor of this point yields an extended continuum characterized by non-simple material behavior and by additional degrees-of-freedom. This includes both standard micromorphic materials as well as inelastic gradient materials as special cases. As in the case of simple materials, the corresponding constitutive relations are subject to restrictions imposed by material frame-indifference and material symmetry. In the latter case, both direct and differential restrictions are obtained in the case of assuming that the free energy density is an isotropic function of its arguments. In addtion, the concept of material isomorphism is shown to extend to inelastic gradient continua, resulting in a gradient generalization of the well-known elastoplastic multiplicative decomposition of the deformation gradient. Finally, we examine the consequences of gradient extension for the formulation of configurational field and balance relations, and in particular for the Eshelby stress. This is carried out with the help of an incremental stress potential formulation as based on a continuum thermodynamic approach to the coupled field problem involved. (Less)
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author
organization
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type
Contribution to journal
publication status
published
subject
keywords
Inelastic gradient microstructure, gradient elastoplastic decomposition, incremental variational approach
in
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
volume
89
issue
8
pages
687 - 697
conference name
Annual GAMM Meeting 2007
external identifiers
  • WOS:000268993500008
  • Scopus:68249146462
DOI
10.1002/zamm.200800171
language
English
LU publication?
yes
id
d65a36b6-dd83-46ae-8948-f9308c95e663 (old id 1477131)
date added to LUP
2012-11-14 20:15:48
date last changed
2016-10-13 05:06:38
@misc{d65a36b6-dd83-46ae-8948-f9308c95e663,
  abstract     = {The purpose of this work is the investigation of some constitutive and configurational aspects of phenomenological model formulations for a class of materials with history-dependent gradient microstructure. The assumption that the behavior of a material point is affected by history-dependent processes in a finite neighbor of this point yields an extended continuum characterized by non-simple material behavior and by additional degrees-of-freedom. This includes both standard micromorphic materials as well as inelastic gradient materials as special cases. As in the case of simple materials, the corresponding constitutive relations are subject to restrictions imposed by material frame-indifference and material symmetry. In the latter case, both direct and differential restrictions are obtained in the case of assuming that the free energy density is an isotropic function of its arguments. In addtion, the concept of material isomorphism is shown to extend to inelastic gradient continua, resulting in a gradient generalization of the well-known elastoplastic multiplicative decomposition of the deformation gradient. Finally, we examine the consequences of gradient extension for the formulation of configurational field and balance relations, and in particular for the Eshelby stress. This is carried out with the help of an incremental stress potential formulation as based on a continuum thermodynamic approach to the coupled field problem involved.},
  author       = {Svendsen, Bob and Neff, Patrizio and Menzel, Andreas},
  keyword      = {Inelastic gradient microstructure,gradient elastoplastic decomposition,incremental variational approach},
  language     = {eng},
  number       = {8},
  pages        = {687--697},
  series       = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik},
  title        = {On constitutive and configurational aspects of models for gradient continua with microstructure},
  url          = {http://dx.doi.org/10.1002/zamm.200800171},
  volume       = {89},
  year         = {2009},
}