WIAS Preprint No. 1127, (2006)

Analytical and numerical methods for finite-strain elastoplasticity



Authors

  • Gürses, Ercan
  • Mainik, Andreas
  • Miehe, Christian
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 74C15 74B20 49J40 49S05

Keywords

  • Multiplicative plasticity, energetic formulation, time-incremental minimization, microstructure, energy relaxation

Abstract

An important class of finite-strain elastoplasticity is based on the multiplicative decomposition of the strain tensor $F=F_el F_pl$ and hence leads to complex geometric nonlinearities. This survey describes recent advances on the analytical treatment of time-incremental minimization problems with or without regularizing terms involving strain gradients. For a regularization controlling all of $nabla F_pl$ we provide an existence theory for the time-continuous rate-independent evolution problem, which is based on a recently developed energetic formulation for rate-independent 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 evolution of such microstructure and discuss algorithms for solving the associated space-time discretizations. We outline in a finite-step-sized incremental setting of standard dissipative materials details of relaxation-induced microstructure development 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.

Appeared in

  • Multifield Problems in Solid and Fluid Mechanics, R. Helmig, A. Mielke, B. Wohlmuth, eds., vol. 28 of Lecture Notes in Applied and Computational Mechanics, Springer, Heidelberg, 2006, pp. 443--481

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