Models of dynamic damage and phase-field fracture, and their various time discretisations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866929508602347520 |
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| author | Roubíček, Tomáš |
| author_facet | Roubíček, Tomáš |
| contents | Several variants of models of damage in viscoelastic continua under small strains in the Kelvin-Voigt rheology are presented and analyzed by using the Galerkin method. The particular case, known as a phase-field fracture approximation of cracks, is discussed in detail. All these models are dynamic (i.e. involve inertia to model vibrations or waves possibly emitted during fast damage/fracture or induced by fast varying forcing) and consider viscosity which is also damageable. Then various options for time discretisation are devised. Eventually, extensions to more complex rheologies or a modification for large strains are briefly exposed, too. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_04110 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Models of dynamic damage and phase-field fracture, and their various time discretisations Roubíček, Tomáš Analysis of PDEs Numerical Analysis 35Q74, 35R45, 65K15, 65M12, 74R20 Several variants of models of damage in viscoelastic continua under small strains in the Kelvin-Voigt rheology are presented and analyzed by using the Galerkin method. The particular case, known as a phase-field fracture approximation of cracks, is discussed in detail. All these models are dynamic (i.e. involve inertia to model vibrations or waves possibly emitted during fast damage/fracture or induced by fast varying forcing) and consider viscosity which is also damageable. Then various options for time discretisation are devised. Eventually, extensions to more complex rheologies or a modification for large strains are briefly exposed, too. |
| title | Models of dynamic damage and phase-field fracture, and their various time discretisations |
| topic | Analysis of PDEs Numerical Analysis 35Q74, 35R45, 65K15, 65M12, 74R20 |
| url | https://arxiv.org/abs/1906.04110 |