$ξ$-Based adaptive phase field model for quasi-static anti-plane fracture
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911006471487488 |
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| author | Fernando, Maria P. Mallikarjunaiah, S. M. |
| author_facet | Fernando, Maria P. Mallikarjunaiah, S. M. |
| contents | The $ξ$-based spatially adaptive three-field variable phase-field model for quasi-static anti-plane crack propagation is introduced. A dynamically optimized regularization length is integrated to improve computational efficiency and accuracy in numerical approximations. A local adaptive mesh refinement strategy is developed, which maintains an optimal balance between mesh resolution and the accurate depiction of fractures using the \textsf{AT1} diffuse interface model. The total energy functional is comprised of three components: strain energy, surface energy, and a third term reliant on the damage zone's regularization length. The governing partial differential equations for mechanics and phase-field variables, derived from Euler-Lagrange, are discretized via the finite-element method. Two parameters functioning as penalty variables are incorporated; both are asymptotically estimated from the gradient of the phase-field variable. By these estimated parameters, mesh adaptivity is enhanced, ensuring the convergence of the numerical solution. Standard phase-field methods are shown by numerical results to be surpassed by the adaptive model; an accurate representation of fractures is provided, and computational costs are significantly lowered. By employing the proposed spatially adaptive approach, a vastly larger regularization length parameter is achieved compared to other methods throughout the entire computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $ξ$-Based adaptive phase field model for quasi-static anti-plane fracture Fernando, Maria P. Mallikarjunaiah, S. M. Numerical Analysis The $ξ$-based spatially adaptive three-field variable phase-field model for quasi-static anti-plane crack propagation is introduced. A dynamically optimized regularization length is integrated to improve computational efficiency and accuracy in numerical approximations. A local adaptive mesh refinement strategy is developed, which maintains an optimal balance between mesh resolution and the accurate depiction of fractures using the \textsf{AT1} diffuse interface model. The total energy functional is comprised of three components: strain energy, surface energy, and a third term reliant on the damage zone's regularization length. The governing partial differential equations for mechanics and phase-field variables, derived from Euler-Lagrange, are discretized via the finite-element method. Two parameters functioning as penalty variables are incorporated; both are asymptotically estimated from the gradient of the phase-field variable. By these estimated parameters, mesh adaptivity is enhanced, ensuring the convergence of the numerical solution. Standard phase-field methods are shown by numerical results to be surpassed by the adaptive model; an accurate representation of fractures is provided, and computational costs are significantly lowered. By employing the proposed spatially adaptive approach, a vastly larger regularization length parameter is achieved compared to other methods throughout the entire computation. |
| title | $ξ$-Based adaptive phase field model for quasi-static anti-plane fracture |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.12360 |