Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

Abstract

SUMMARYCrack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.

Effects of spatial heterogeneity and material anisotropy on the fracture pattern and macroscopic effective toughness of Mancos Shale in Brazilian tests

“…Both solid displacement field and phase field are the explicit function of position within the body Ω. A variety of phase field models has been applied for many engineering applications in quasi‐static and dynamic regimes [ Bourdin et al ., ; Miehe et al ., ; Hofacker and Miehe , , ], ductile or brittle fractures [ Ambati et al ., ; Verhoosel and Borst , ], anisotropic surface energy fracture [ Li et al ., ], and fluid‐filled fracture [ Wick et al ., ]. The phase field approach numerically replicates the Brazilian test effectively because it does not require the crack path to be predetermined or straight, and it can handle crack coalescence and branching relatively easily.…”

Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants

“…Models showing an intrinsic high computational cost such as the phase-field approaches can particularly benefit from this concept due to the easy parallelization of the algorithms presented. The approximation of phase-field models with LME in biomembrane dynamics [32,33] and fracture mechanics [35,36] are successful examples of these optimization procedures.…”

“…Because the LME basis functions do not satisfy the Kronecker-delta property at nodes, these schemes are referred to as approximants instead of interpolants. The capabilities of LME approximants have been examined in a variety of computational mechanics applications, such as linear and nonlinear elasticity [25,26], plate [27] and thin-shell analysis [28,29], convection-di↵usion problems [30,31], and phase-field models of biomembranes [32,33] and fracture mechanics [34,35,36].…”

Phase transformation and fracture in single LixFePO4cathode particles: a phase-field approach to Li–ion intercalation and fracture

“…Therefore, the phase-field fracture method should be modified to incorporate anisotropic surface energies into the Griffith's criterion G c = 2γ. There has been some very recent work along these lines [26] doing just that. In their work the authors incorporate a strongly anisotropic surface energy into the phase-field fracture model.…”