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This paper is concerned with a phenomenological model of initially isotropic finite-strain multiplicative elasto-plasticity for polycrystals with grain boundary relaxation (Neff, Cont. Mech. Thermo., 2003). We prove a local in time existence and uniqueness result of the corresponding initial boundary value problem in the quasistatic rate-dependent case. Use is made of a generalized Korn first inequality (Neff, Proc. Roy. Soc. Edinb. A, 2002) taking into account the incompatibility of the plastic deformation Fp, This is a first result concerning classical solutions in geometrically exact nonlinear finite visco-plasticity for polycrystals. Global existence is not proved and cannot be expected due to the natural possibility of material degradation in time.

Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation