Linearization of quasistatic fracture evolution in brittle materials
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910706071240704 |
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| author | Friedrich, Manuel Steinke, Pascal Stinson, Kerrek |
| author_facet | Friedrich, Manuel Steinke, Pascal Stinson, Kerrek |
| contents | We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution of quasistatic crack growth in linear elasticity without any a priori assumptions on the geometry of the crack set. This result corresponds to the evolutionary counterpart of the static linearization result by the first author, where a Griffith model for nonsimple brittle materials has been considered featuring an elastic energy which also depends suitably on the second gradient of the deformations. The proof relies on a careful study of unilateral global minimality, as determined by the nonlinear evolutionary problem, and its linearization together with a variant of the jump transfer lemma in GSBD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linearization of quasistatic fracture evolution in brittle materials Friedrich, Manuel Steinke, Pascal Stinson, Kerrek Analysis of PDEs Functional Analysis 49J45, 70G75, 74B10, 74B20, 74G65, 74R10 We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution of quasistatic crack growth in linear elasticity without any a priori assumptions on the geometry of the crack set. This result corresponds to the evolutionary counterpart of the static linearization result by the first author, where a Griffith model for nonsimple brittle materials has been considered featuring an elastic energy which also depends suitably on the second gradient of the deformations. The proof relies on a careful study of unilateral global minimality, as determined by the nonlinear evolutionary problem, and its linearization together with a variant of the jump transfer lemma in GSBD. |
| title | Linearization of quasistatic fracture evolution in brittle materials |
| topic | Analysis of PDEs Functional Analysis 49J45, 70G75, 74B10, 74B20, 74G65, 74R10 |
| url | https://arxiv.org/abs/2411.13446 |