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SIAM Journal on Mathematical Analysis· 2026Q1

Well-Posedness of Discretizations for Fractional Elasto-Plasticity

Michael Feischl, David Niederkofler, Barbara I. Wohlmuth

Short summary

This paper proves the well-posedness of an explicit-in-time discretization for fractional elasto-plasticity models, combining it with a finite element method in space.

AI-generated from the title and abstract; the full text is not read.

Key points

  • Proposes explicit and implicit discretizations for fractional elasto-plasticity models.
  • Demonstrates well-posedness for explicit-in-time discretization combined with finite elements in space.
  • Utilizes radial return mapping and exploits the finite support of the kernel.
  • Presents 2D and 3D numerical results illustrating algorithm performance and fractional parameter influence.

AI-generated from the title and abstract; the full text is not read.

Abstract

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 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.

The authors' abstract, as published at the source. SIAM Journal on Mathematical Analysis, 2026 · DOI ↗

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Field: Modeling and Simulation

Modeling and SimulationMathematics