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A Model for the Evolution of Laminates
Author(s) -
Hackl Klaus,
Heinz Sebastian,
Mielke Alexander
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910012
Subject(s) - microstructure , convexity , simple (philosophy) , extension (predicate logic) , minification , task (project management) , variable (mathematics) , state variable , computer science , mathematics , mathematical optimization , materials science , mathematical analysis , physics , composite material , economics , thermodynamics , epistemology , philosophy , management , financial economics , programming language
We study the time evolution of a generalized standard material in elastoplasticity. Of our particular interest are the formation and the evolution of microstructure. Our aim is to prove the existence of solutions. This is a challenging task, since the presence of microstructure comes along with a lack of convexity and, hence, compactness arguments cannot be applied to prove the existence of solutions. In order to overcome this problem, we will incorporate information on the microstructure into the internal variable, which is still compatible with the notion of generalized standard materials. More precisely, we shall allow such forms of microstructure that are given by simple laminates. We will consider a model for the evolution of these laminates and we will state a result on the existence of solutions to the time‐incremental minimization problem. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)