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

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Author

Summary, in English

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.

Department/s

Publishing year

2009

Language

English

Pages

687-697

Publication/Series

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volume

89

Issue

8

Document type

Journal article

Publisher

John Wiley & Sons Inc.

Topic

  • Mechanical Engineering

Keywords

  • Inelastic gradient microstructure
  • gradient elastoplastic decomposition
  • incremental variational approach

Conference name

International Congress on Industrial Applied Mathematics and GAMM Annual Meeting, 2007

Conference date

2007-07-16 - 2007-07-20

Conference place

Zurich, Switzerland

Status

Published

ISBN/ISSN/Other

  • ISSN: 0044-2267