Phase field modeling of fracture in anisotropic brittle solids

The concept of representative crack elements for phase‐field fracture: Anisotropic elasticity and thermo‐elasticity

“…The introduction of a crack orientation is not unique and requires a concept, also for its evolution and irreversibility. The models in Section 2, which rely on the information about the crack orientation, use one of the following three approaches: direction of phase‐field gradient, maximum absolute principle stress direction, direction by principle of maximum dissipated energy …”

“…Also in Teichtmeister et al, Bryant and Sun, and Levitas et al, considerations on the crack kinematics are used with the aim to obtain a consistent material degradation for the phase‐field method. In those approaches, a crack orientation is explicitly introduced into the phase‐field method.…”

Coupled phase‐field modeling of domain and fracture evolution in anisotropic ferroelectric ceramics

“…2 of 2 Section 7: Coupled problems As constitutive equations we employ an electromechanical stored-energy function Ψ as well as a transversely isotropic cracksurface-density function γ (α, ∇α; A) [6] based on the structural tensor A := 1 + β a ⊗ a with a = 1 and β ∈ ] − 1, ∞[…”

“…Both, fracturing and domain evolution will be modeled by means of phase fields. In the latter work, crack propagation was linked to an anisotropic fracture toughness that enters the model by means of an anisotropic crack-surface-density function (see also Teichtmeister et al [6] for more details). For the modeling of crack propagation we make use of the phase-field approach to fracturing proposed by Miehe et al [2,3].…”

An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture

“…Instead, the effective, possibly anisotropic crack resistance is our quantity of interest. The latter may be used in a phase‐field crack model on the macroscale.…”