We propose a model of finite strain gradient plasticity including phenomenological Prager type linear kinematical hardening and nonlocal kinematical hardening due to dislocation interaction. Based on the multiplicative decomposition, a thermodynamically admissible flow rule for Fp is described involving as plastic gradient Curl Fp. The formulation is covariant w.r.t. superposed rigid rotations of the reference, intermediate and spatial configuration but the model is not spin-free due to the nonlocal dislocation interaction and cannot be reduced to a dependence on the plastic metric [Formula: see text]. The linearization leads to a thermodynamically admissible model of infinitesimal plasticity involving only the Curl of the nonsymmetric plastic distortion p. Linearized spatial and material covariance under constant infinitesimal rotations is satisfied. Uniqueness of strong solutions of the infinitesimal model is obtained if two non-classical boundary conditions on the plastic distortion p are introduced: [Formula: see text] on the microscopically hard boundary ΓD ⊂ ∂Ω and [ Curl p] · τ = 0 on the microscopically free boundary ∂Ω\ΓD, where τ are the tangential vectors at the boundary ∂Ω. A weak reformulation of the infinitesimal model allows for a global in-time solution of the rate-independent initial boundary value problem. The method is based on a mixed variational inequality with symmetric and coercive bilinear form. We use a new Hilbert-space suitable for dislocation density dependent plasticity.
The existence theory to an internal variable model for viscoelastic or viscoplastic solids at small strain is studied. The model consists of an initial–boundary value problem to a system of linear partial differential equations coupled with nonlinear ordinary differential equations. It belongs to the subclass of monotone type models, which typically describe solids with rate dependent behavior exhibiting nonlinear hardening. The monotone type class includes all generalized standard materials. Solutions are found in Lp and [Formula: see text], the proof is based on monotonicity properties.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.