Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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

Svendsen, Bob ; Neff, Patrizio and Menzel, Andreas LU (2009) International Congress on Industrial Applied Mathematics and GAMM Annual Meeting, 2007 In ZAMM Zeitschrift fur 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)
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Inelastic gradient microstructure, gradient elastoplastic decomposition, incremental variational approach
in
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
volume
89
issue
8
pages
687 - 697
publisher
John Wiley & Sons Inc.
conference name
International Congress on Industrial Applied Mathematics and GAMM Annual Meeting, 2007
conference location
Zurich, Switzerland
conference dates
2007-07-16 - 2007-07-20
external identifiers
  • wos:000268993500008
  • scopus:68249146462
ISSN
0044-2267
DOI
10.1002/zamm.200800171
language
English
LU publication?
yes
id
d65a36b6-dd83-46ae-8948-f9308c95e663 (old id 1477131)
date added to LUP
2016-04-01 11:40:42
date last changed
2021-04-13 05:54:05
@article{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},
  issn         = {0044-2267},
  language     = {eng},
  number       = {8},
  pages        = {687--697},
  publisher    = {John Wiley & Sons Inc.},
  series       = {ZAMM Zeitschrift fur 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},
  doi          = {10.1002/zamm.200800171},
  volume       = {89},
  year         = {2009},
}