Well-Posedness of Discretizations for Fractional Elasto-Plasticity
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910909181460480 |
|---|---|
| author | Feischl, Michael Niederkofler, David Wohlmuth, Barbara |
| author_facet | Feischl, Michael Niederkofler, David Wohlmuth, Barbara |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-Posedness of Discretizations for Fractional Elasto-Plasticity Feischl, Michael Niederkofler, David Wohlmuth, Barbara Numerical Analysis 26A33, 74H15, 74H20, 74S05 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. |
| title | Well-Posedness of Discretizations for Fractional Elasto-Plasticity |
| topic | Numerical Analysis 26A33, 74H15, 74H20, 74S05 |
| url | https://arxiv.org/abs/2504.08450 |