Homogenization for dislocation based gradient visco-plasticit

2013/01/14 by Sergiy Nesenenko, Nesenenko, Sergiy · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1301.2911

openalex publication_date 2013/01/14 · arxiv created 2016/10/10 · arxiv updated 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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/Witsch, we derive uniform estimates for the solutions of quasistatic initial-boundary value problems under consideration and then using an unfolding operator technique and a monotone operator method we obtain the homogenized system of equations.

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• Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening

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