Adaptive finite element approximation for quasi-static crack growth
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908281085100032 |
|---|---|
| author | Crismale, Vito Friedrich, Manuel Seutter, Joscha |
| author_facet | Crismale, Vito Friedrich, Manuel Seutter, Joscha |
| contents | We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the triangulation is a part of the unknown of the problem and adaptive in each minimization step. The limit passage is conducted simultaneously in the vanishing mesh size and discretized time step, and results in an evolution for the continuum Griffith model of brittle fracture with isotropic surface energy [FriedrichSolombrino16] which is characterized by an irreversibility condition, a global stability, and an energy balance. Our result corresponds to an evolutionary counterpart of the static Gamma-convergence result in [BabadjianBonhomme23] for which, as a byproduct, we provide an alternative proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive finite element approximation for quasi-static crack growth Crismale, Vito Friedrich, Manuel Seutter, Joscha Analysis of PDEs We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the triangulation is a part of the unknown of the problem and adaptive in each minimization step. The limit passage is conducted simultaneously in the vanishing mesh size and discretized time step, and results in an evolution for the continuum Griffith model of brittle fracture with isotropic surface energy [FriedrichSolombrino16] which is characterized by an irreversibility condition, a global stability, and an energy balance. Our result corresponds to an evolutionary counterpart of the static Gamma-convergence result in [BabadjianBonhomme23] for which, as a byproduct, we provide an alternative proof. |
| title | Adaptive finite element approximation for quasi-static crack growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.18664 |