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arXiv · 2504.08450

Well-Posedness of Discretizations for Fractional Elasto-Plasticity

Michael Feischl·David Niederkofler·Barbara Wohlmuth
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Abstract

We consider a fractional plasticity model based on linear isotropic and kinematic hardening as well as a standard von-Mises yield function, where the flow rule is replaced by a Riesz--Caputo fractional derivative. The resulting mathematical model is typically non-local and non-smooth. Our numerical algorithm is based on the well-known radial return mapping and exploits that the kernel is finitely supported. We propose explicit and implicit discretizations of the model and show the well-posedness of the explicit in time discretization in combination with a standard finite element approach in space. Our numerical results in 2D and 3D illustrate the performance of the algorithm and the influence of the fractional parameter.

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Michael Feischl, David Niederkofler, Barbara Wohlmuth. 2025-04-11. Well-Posedness of Discretizations for Fractional Elasto-Plasticity. https://arxiv.org/abs/2504.08450

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