A phase‐field method for modeling cracks with frictional contact

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.

An extended/generalized phase‐field finite element method for crack growth with global‐local enrichment

“…Numerous tension‐compression asymmetry models have been proposed in the literature (see Li et al [section 3] for a comparison of several phase‐field‐like models of fracture). An alternative can be found in the recent formulation from Fei and Choo which is found to be particularly well suited for frictional contact. In this article, however, the spectral decomposition scheme of Miehe et al is adopted which decomposes the strain tensor into positive and negative parts where ⟨⊙⟩ ± =(⊙±|⊙|)/2; { ε a } a =1… n are the principal strains and { n a } a =1… n the principal strain directions which are orthogonal due to the symmetry of ε , that is, n a · n b =δ ab .…”

Phase-field modeling of geologic fracture incorporating pressure-dependence and frictional contact

“…Recently, the authors have developed the first way to incorporate frictional contact into a phase-field fracture [11]. The key idea is to compute the stress tensor inside an interface region, which is diffusely approximated by the phase field, according to the contact condition.…”

“…This section briefly presents representative examples to demonstrate the capabilities of the two new phase-field models. Detailed descriptions of the following examples can be found in [10,11].…”

“…Nevertheless, no computational model had been reported to be capable of simulating hybrid fracture, let alone its manifestation during the transition from extension to shear fracture. To investigate whether the coupled phase-field and plasticity model captures the pressure-induced transition of fracturing modes including hybrid fracture, tension tests on dogbone-shape laboratory-scale specimens -as done by Ramsey and Chester [11] were simulated at different confining pressures. The simulation results are shown in Fig.…”

“…Herein, the essence of the new models' formulations and verification and validation results are presented. For more detailed descriptions of the models, please refer to journal publications [10,11].…”