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Analytical and numerical methods for finite-strain elastoplasticity

Gürses, Ercan
Mainik, Andreas
Miehe, Christian
Mielke, Alexander
An important class of finite-strain elastoplasticity is based on the multiplicative decomposition of the strain tensor F = Fel Fpl and hence leads to complex geometric nonlinearities. This survey describes recent advances in the analytical treatment of time-incremental minimization problems with or without regularizing terms involving strain gradients. For a regularization controlling all of ∇ Fpl we provide an existence theory for the time-continuous rate-independent evolution problem, which is based on a recently developed energetic formulation for rateindependent systems in abstract topological spaces. In systems without gradient regularization one encounters the formation of microstructures, which can be described by sequential laminates or more general gradient Young measures. We provide a mathematical framework for the evo lution of such microstructures and discuss algorithms for solving the associated spacetime discretizations. In a finite-step-sized incremental setting of standard dissipative materials (also called generalized standard materials) we outline also details of relaxation-induced microstructure developments for strain softening von Mises plasticity and single-slip crystal plasticity. The numerical implementations are based on simplified assumptions concerning the complexity of the microstructures. © Springer-Verlag Berlin Heidelberg 2006.