New Paper: A phase-field method for modeling cracks with frictional contact

Our paper on a phase-field method for frictional cracks has been accepted for publication in the International Journal for Numerical Methods in Engineering. Big congratulations to Frank on his very first publication!

Read the paper: Fei and Choo, IJNME 2019.

Abstract: We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent arbitrary crack geometry without an explicit function or basis enrichment, and (2) it does not require an algorithm for imposing contact constraints. The first feature, which is common in phase-field models of fracture, is attained by regularizing a sharp interface geometry using a surface density functional. The second feature, which is a unique advantage for contact problems, is achieved by a new approach that calculates the stress tensor in the regularized interface region depending on the contact condition of the interface. Particularly, under a slip condition, this approach updates stress components in the slip direction using a standard contact constitutive law, while making other stress components compatible with stress in the bulk region to ensure non-penetrating deformation in other directions. We verify the proposed phase-field method using stationary interface problems simulated by discrete methods in the literature. Subsequently, by allowing the phase field to evolve according to brittle fracture theory, we demonstrate the proposed method's capability for modeling crack growth with frictional contact.

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This work develops the first phase-field method for modeling cracks and discontinuities with frictional contact. Such frictional interfaces are omnipresent in many engineering problems; notable examples in geotechnical engineering are slip surfaces and geologic faults. Yet computational modeling of frictional interfaces has been a notoriously challenging problem, because it has required a sophisticated algorithm for imposing contact constraints on a discontinuous entity. Here, we propose a phase-field method that can bypass the necessity of a contact algorithm, by modeling a frictional interface as a continuum problem with heterogeneous stiffness. In the figures above, the phase-field method has been verified with results from the XFEM as well as the classic FEM. Notably, the proposed method produces non-oscillatory contact stresses even along an embedded discontinuity, thanks to its algorithm-free nature.

This work develops the first phase-field method for modeling cracks and discontinuities with frictional contact. Such frictional interfaces are omnipresent in many engineering problems; notable examples in geotechnical engineering are slip surfaces and geologic faults. Yet computational modeling of frictional interfaces has been a notoriously challenging problem, because it has required a sophisticated algorithm for imposing contact constraints on a discontinuous entity. Here, we propose a phase-field method that can bypass the necessity of a contact algorithm, by modeling a frictional interface as a continuum problem with heterogeneous stiffness. In the figures above, the phase-field method has been verified with results from the XFEM as well as the classic FEM. Notably, the proposed method produces non-oscillatory contact stresses even along an embedded discontinuity, thanks to its algorithm-free nature.