Abstract
We study finite-strain elastoplasticity in a new formulation proposed in [8,1,7]. This theory does not need smoothness and is based on energy minimization techniques. In particular, it gives rise to robust algorithms. It is based on two scalar constitutive functions: an elastic potential and a dissipation potential which give rise to an energy functional and a dissipation distance.
Here we study these dissipation distances in some detail and present situations where they are quite explicitly available. These include isotropic plasticity of Prandtl-Reuß type and examples from two-dimensional single-crystal plasticity. We put special emphasis on the geometric nonlinearities arising from the underlying matrix groups which lead to optimization problems on Lie groups.
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Hackl, K., Mielke, A., Mittenhuber, D. (2003). Dissipation distances in multiplicative elastoplasticity. In: Wendland, W., Efendiev, M. (eds) Analysis and Simulation of Multifield Problems. Lecture Notes in Applied and Computational Mechanics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36527-3_8
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DOI: https://doi.org/10.1007/978-3-540-36527-3_8
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