On constitutive and configurational aspects of models for gradient continua with microstructure
(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:
https://lup.lub.lu.se/record/1477131
- author
- Svendsen, Bob ; Neff, Patrizio and Menzel, Andreas LU
- organization
- publishing date
- 2009
- 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
- Wiley-VCH Verlag
- 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
- 2025-04-04 15:13:15
@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}},
keywords = {{Inelastic gradient microstructure; gradient elastoplastic decomposition; incremental variational approach}},
language = {{eng}},
number = {{8}},
pages = {{687--697}},
publisher = {{Wiley-VCH Verlag}},
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}},
}