Phase-field finite deformation fracture with an effective energy for regularized crack face contact
EntityUAM. Departamento de Matemáticas
10.1016/j.jmps.2022.104994Journal of the Mechanics and Physics of Solids 167 (2022): 104994
ISSN0022-5096 (print); 1873-4782 (online)
Funded byAgencia Estatal de Investigación of the Spanish Ministry Research and Innovation (Project MTM2017-85934-C3-2-P)
ProjectGobierno de España. MTM2017-85934-C3-2-P
SubjectsCrack Faces; Crack-Face Traction; Effective Energy; Gram-Schmidt; Gram–Schmidt Decomposition; Schmidt Decomposition; Matemáticas
Rights© 2022 The Author(s)
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Phase-field models are a leading approach for realistic fracture problems. They treat the crack as a second phase and use gradient terms to smear out the crack faces, enabling the use of standard numerical methods for simulations. This regularization causes cracks to occupy a finite volume in the reference, and leads to the inability to appropriately model the closing or contacting – without healing – of crack faces. Specifically, the classical idealized crack face tractions are that the shear component is zero, and that the normal component is zero when the crack opens and identical to the intact material when the crack closes. Phase-field fracture models do not replicate this behavior. This work addresses this shortcoming by introducing an effective crack energy density that endows the regularized (finite volume) phase-field crack with the effective properties of an idealized sharp crack. The approach is based on applying the QR (upper triangular) decomposition of the deformation gradient tensor in the basis of the crack, enabling a transparent identification of the crack deformation modes. By then relaxing over those modes that do not cost energy, an effective energy is obtained that has the intact response when the crack faces close and zero energy when the crack faces are open. The effective energy is often, but not always, consistent with the classical crack-face tractions; it is shown here that there generally does not exist a stored energy that is consistent both with the classical crack-face tractions and with reproducing the intact response when the crack closes. A highlight of this approach is that it lies completely in the setting of finite deformation, enabling potential application to soft materials and other settings with large deformation or rotations. The model is applied to numerically study representative complex loadings, including (1) cyclic loading on a cavity in a soft solid that shows the growth and closing of cracks in complex stress states; and (2) cyclic shear that shows a complex pattern of crack branching driven by the closure of cracks
Google Scholar:Hakimzadeh, Maryam - Agrawal, Vaibhav - Dayal, Kaushik - Mora Corral, Carlos
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