Sharp-crack limit of a phase-field model for brittle fracture |
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Authors: | Milton N da Silva Jr Fernando P Duda Eliot Fried |
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Institution: | 1. Programa de Engenharia Mecânica, COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Cidade Universitária, Rio de Janeiro, Cx. Postal 68503 21945-970, Brazil;2. Department of Mechanical Engineering, McGill University, Montréal, Québec, Canada H3A 2K6 |
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Abstract: | A matched asymptotic analysis is used to establish the correspondence between an appropriately scaled version of the governing equations of a phase-field model for fracture and the equations of the two-dimensional sharp-crack theory of Gurtin and Podio-Guidugli (1996) that arise on assuming that the bulk constitutive behavior is nonlinearly elastic, requiring that surface energy provides the only factor limiting crack propagation, and assuming that the fracture kinetics are isotropic. Consistent with the prominence of the configurational momentum balance at the crack tip in the latter theory, the approach capitalizes on the configurational momentum balance that arises naturally in the context of the phase-field model. The model developed and utilized here incorporates irreversibility of the phase-field evolution. This is achieved by introducing a suitable constraint and by carefully heeding the influence of that constraint on the kinetics underlying microstructural changes associated with fracture. The analysis is predicated on the assumption that the phase-field variable takes values in the closed interval between zero and unity. |
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Keywords: | Crack propagation Configurational forces J-integral Griffith criterion Internal constraints |
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