A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

By C. Miehé, M. Hofacker, F. Welschinger. 2010

2,872 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/94736159e40564b00a2c13fff93d8cdec01cf505

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In Mechanics of Materials

Citations in the corpus

A phase-field/gradient damage model for brittle fracture in elastic–plastic solids (2015, background): “[27], for time integration of the resulting semi-discrete evolution equations.”
Phase-field modeling of fluid-driven dynamic cracking in porous media (2019, background): “For 2D and 3D problems, the crack surface density per unit volume of the solid is given by [31] γ(φ,▽φ) = φ 2 2l0 + l0 2 ∂φ ∂xi ∂φ ∂xi (8) Thus, exploiting Eq.”
Phase-field modelling of interface failure in brittle materials (2019, methodology): “The resulting non-linear equations are solved using a staggered scheme [12].”
A phase‐field model for cohesive fracture (2013, background): “As in [21, 22] we consider the approximated Dirac function δǫ(xn) = 1 2ǫ exp ( − |xn| ǫ ) (11) with ǫ > 0 a length scale parameter.”
Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model (2016, methodology): “In particular, mesh refinement allows us to perform systematic studies with respect to the spatial discretization parameter.”
Phase field modelling of anisotropic crack propagation (2017, background): “It can be shown (see e.g. Miehe et al. (2010)) that such a function can be determined by solving the following boundary value problem on Ω: d− `2∆d = 0 in Ω, d(x) = 1 on Γ, ∇d(x) ·n = 0 on ∂Ω, (1) where ∆(.) is the Laplacian, ` is a regularization parameter describing the actual width of the…”
A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts (2018, positive): “…extended continuum formulations are conceptually in line with phase-field modeling approaches, which have recently also become very popular as a spatially regularized method of modeling fracture (Ambati et al., 2015; Borden et al., 2012; Kuhn et al., 2016; Miehe et al., 2010a, 2016, 2010b).”
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications (2019, background): “The strain-history functional can be used to define initial cracks in the system [34].”
Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation (2017, background): “[50, 53] added more physical explanation and modifications to the original model, yielding a so-called phase-field formulation for fracture propagation.”