Bond failure in peridynamics: Nonequivalence of critical stretch and critical energy density criteria
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908829977935872 |
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| author | Seleson, Pablo Stinga, Pablo Raúl Vaughan, Mary |
| author_facet | Seleson, Pablo Stinga, Pablo Raúl Vaughan, Mary |
| contents | This paper rigorously analyzes bond failure in the peridynamic theory of solid mechanics, which is a fundamental component of fracture modeling. We compare analytically and numerically two common bond-failure criteria:~{\em critical stretch} and~{\em critical energy density}. In the former, bonds fail when they stretch to a critical value, whereas in the latter, bonds fail when the bond energy density exceeds a threshold. By focusing the analysis on bond-based models, we prove mathematically that the critical stretch criterion and the critical energy density criterion are not equivalent in general and result in different bond-breaking and fracture phenomena. Numerical examples showcase the striking differences between the effect of the two criteria on crack dynamics, including the crack tip evolution, crack propagation, and crack branching. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_12061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bond failure in peridynamics: Nonequivalence of critical stretch and critical energy density criteria Seleson, Pablo Stinga, Pablo Raúl Vaughan, Mary Materials Science Analysis of PDEs 74A70, 74R10, 74A45, 45K05, 65R20 This paper rigorously analyzes bond failure in the peridynamic theory of solid mechanics, which is a fundamental component of fracture modeling. We compare analytically and numerically two common bond-failure criteria:~{\em critical stretch} and~{\em critical energy density}. In the former, bonds fail when they stretch to a critical value, whereas in the latter, bonds fail when the bond energy density exceeds a threshold. By focusing the analysis on bond-based models, we prove mathematically that the critical stretch criterion and the critical energy density criterion are not equivalent in general and result in different bond-breaking and fracture phenomena. Numerical examples showcase the striking differences between the effect of the two criteria on crack dynamics, including the crack tip evolution, crack propagation, and crack branching. |
| title | Bond failure in peridynamics: Nonequivalence of critical stretch and critical energy density criteria |
| topic | Materials Science Analysis of PDEs 74A70, 74R10, 74A45, 45K05, 65R20 |
| url | https://arxiv.org/abs/2602.12061 |