Well-Posedness of Discretizations for Fractional Elasto-Plasticity

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 nonlocal and nonsmooth. 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.