Homogenization for dislocation based gradient visco-plasticity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Nesenenko, Sergiy

关键词: Gradient plasticity;    Dislocations;    Homogenization;    Periodic unfolding;    Horn's inequality;    Rate-dependent models;   

DOI  :  10.1016/j.jmaa.2014.10.056

来源: Elsevier

【 摘 要 】

In this work we study the homogenization for infinitesimal dislocation based gradient viscoplasticity with linear kinematic hardening and general non-associative monotone plastic flows. The constitutive equations in the models we study are assumed to be only of monotone type. Based on the generalized version of Korn's inequality for incompatible tensor fields (the non-symmetric plastic distortion) due to Neff/Pauly/Witch, we derive uniform estimates for the solutions of quasistatic initial-boundary value problems under consideration and then using a modified unfolding operator technique and a monotone operator method we obtain the homogenized system of equations. A new unfolding result for the Curl Curl-operator is presented in this work as well. The proof of the last result is based on the Helmholtz-Weyl decomposition for vector fields in general La-spaces. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free