A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913786542161920 |
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| author | Kienle, Daniel Keip, Marc-Andre |
| author_facet | Kienle, Daniel Keip, Marc-Andre |
| contents | A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is modeled by means of a phase-field approach to fracture, plastic effects are taken into account by using a Drucker-Prager-type yield-criterion function. This yield-criterion function governs the plastic evolution of the fluid-solid mixture. Fluid storage and transport are described by a Darcy-Biot-type formulation. Thereby the fluid storage is decomposed into a contribution due to the elastic deformations and one due to the plastic deformations. A local return mapping scheme is used for the update of the plastic quantities. The global minimization structure demands a $H($div$)$-conforming finite-element formulation. Furthermore this is combined with an enhanced-assumed-strain formulation in order to overcome locking phenomena arising from the plastic deformations. The robustness and capabilities of the presented framework will be shown in a sequence of numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_14970 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids Kienle, Daniel Keip, Marc-Andre Numerical Analysis Other Condensed Matter A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is modeled by means of a phase-field approach to fracture, plastic effects are taken into account by using a Drucker-Prager-type yield-criterion function. This yield-criterion function governs the plastic evolution of the fluid-solid mixture. Fluid storage and transport are described by a Darcy-Biot-type formulation. Thereby the fluid storage is decomposed into a contribution due to the elastic deformations and one due to the plastic deformations. A local return mapping scheme is used for the update of the plastic quantities. The global minimization structure demands a $H($div$)$-conforming finite-element formulation. Furthermore this is combined with an enhanced-assumed-strain formulation in order to overcome locking phenomena arising from the plastic deformations. The robustness and capabilities of the presented framework will be shown in a sequence of numerical examples. |
| title | A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids |
| topic | Numerical Analysis Other Condensed Matter |
| url | https://arxiv.org/abs/2103.14970 |