Homogenization of rate-dependent inelastic models of monotone type

Article type: Research Article

Authors: Nesenenko, Sergiy

Affiliations: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany. Tel.: +49 6151 16 2788; E-mail: nesenenko@mathematik.tu-darmstadt.de | Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Campus Essen, Universitätsstr. 2, 45141 Essen, Germany. Tel.: +49 201 183 2173

Abstract: Using the periodic unfolding method we derive the homogenized equations for the quasi-static initial boundary value problem with internal variables, which model the deformation behavior of viscoplastic materials with a periodic microstructure. The free energy associated with the problem is allowed to be positive semi-definite.

Keywords: homogenization, plasticity, unfolding method, viscoplasticity, maximal monotone operator, periodic microstructure

DOI: 10.3233/ASY-2012-1108

Journal: Asymptotic Analysis, vol. 81, no. 1, pp. 1-29, 2013