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Exploitation of Configurational Forces in Extended Nonlocal Continua with Microstructure
Author(s) -
Frankenreiter Ilona,
Zimmermann Dominik,
Miehe Christian
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810421
Subject(s) - macro , space (punctuation) , finite element method , position (finance) , physics , dual (grammatical number) , field (mathematics) , mathematical analysis , classical mechanics , statistical physics , mechanics , mathematics , computer science , thermodynamics , pure mathematics , art , literature , finance , economics , programming language , operating system
We investigate aspects of the application of configurational forces in extended nonlocal continua with microstructure. Focussing on multifield approaches to gradient–type inelastic solids, the coupled problem is governed by the macroscopic deformation field, while nonlocal inelastic effects on the microstructure are described by a family of order parameter fields. The dual macro– and micro–field equations are derived within an incremental variational framework. Using an incremental principle, due to the variation with respect to the material position, an additional balance in the material space appears with the dual macro–micro–balances in the physical space. In view of the numerical implementation of this coupled problem by a finite element method, the incremental variational framework is recast into a discrete format in terms of discrete macro– and micro–physical nodal forces and configurational nodal forces. Applying a staggered solution scheme, the configurational branch is used as a postprocessing procedure with all the ingredients known from the solution of the coupled macro–micro–problem. The procedure is implemented for a nonlocal, viscous damage model. The consequences with regard to the configurational nodal forces are assessed by means of a numerical example. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)