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Homogenization in the Theory of Viscoplasticity
Author(s) -
Nesenenko Sergiy
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510020
Subject(s) - homogenization (climate) , quasistatic process , viscoplasticity , monotonic function , mathematics , mathematical analysis , differential inclusion , boundary value problem , nonlinear system , partial differential equation , asymptotic homogenization , physics , constitutive equation , finite element method , thermodynamics , algorithm , composite number , biodiversity , ecology , quantum mechanics , biology
We study the homogenization of the quasistatic initial boundary value problem with internal variables which models the deformation behavior of viscoplastic bodies with a periodic microstructure. This problem is represented through a system of linear partial differential equations coupled with a nonlinear system of differential equations or inclusions. Recently it was shown by Alber [2] that the formally derived homogenized initial boundary value problem has a solution. From this solution we construct an asymptotic solution for the original problem and prove that the difference of the exact solution and the asymptotic solution tends to zero if the lengthscale of the microstructure goes to zero. The work is based on monotonicity properties of the differential equations or inclusions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)