Abstract
Solid materials react in an elastic way to sufficiently small forces, but when these exceed a threshold, remaining plastic deformations occur. Simple mathematical descriptions lead to nonsmooth evolution problems that can be approximated by sequences of convex minimization problems. Related quasioptimal a priori and a posteriori error estimates for low-order finite element methods are derived. The numerical implementation requires solving a nonlinear, nonsmooth equation at every time step whose realization is based on eliminating the plastic strain. Short codes that realize different types of plastic material behavior are provided.
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Bartels, S. (2015). Elastoplasticity. In: Numerical Methods for Nonlinear Partial Differential Equations. Springer Series in Computational Mathematics, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-13797-1_11
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DOI: https://doi.org/10.1007/978-3-319-13797-1_11
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