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Material Forces in Standard Dissipative Solids obtained from an Incremental Variational Formulation
Author(s) -
Zimmermann Dominik,
Miehe Christian
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410118
Subject(s) - dissipative system , context (archaeology) , minification , variational principle , classical mechanics , constitutive equation , work (physics) , rigid body , boundary value problem , mathematics , mathematical analysis , physics , mathematical optimization , finite element method , thermodynamics , paleontology , biology
A variational method for the definition of material forces in standard dissipative solids based on a path‐dependent incremental minimization structure is proposed. The underlying base is provided by incremental variational formulations for standard dissipative solids. For this type of inelastic constitutive response, an incremental stress potential can be constructed by a constitutive minimization principle. Then, the incremental boundary value problem of a deformed inelastic body is governed by a minimization principle. In this context dual variational settings for the definition of both the physical as well as the material forces are presented. This yields to the definition of material forces as the sensitivity of work with respect to change of Lagrangian, i.e. material coordinates. An application of the material force method to the description of elastic‐plastic fracture mechanics is given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)