Repository: Freie Universität Berlin, Math Department

Global existence results for viscoplasticity at finite strain

Mielke, A. and Rossi, R. and Savaré, G. (2018) Global existence results for viscoplasticity at finite strain. Archive for Rational Mechanics and Analysis, 227 (1). pp. 423-475. ISSN Print: 0003-9527; Online: 1432-0673


Official URL:


We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate, and thus depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance and energy-dissipation-inequality solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

Item Type:Article
Additional Information:Preprint 09/2016: WIAS Preprint No. 2304
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2174
Deposited By: Silvia Hoemke
Deposited On:08 Jan 2018 09:20
Last Modified:08 Jan 2018 09:20

Repository Staff Only: item control page