A detailed investigation of the model influencing parameters of the phase‐field fracture approach

Abstract

Phase-field approaches to fracture are gaining popularity to compute a priori unknown crack paths. In this work the sensitivity of such phase-field approaches with respect to its model specific parameters, that is, the critical length of regularization, the degradation function and the mobility, is investigated. The susceptibility of the computed cracks to the setting of these parameters is studied for problems of linear and finite elasticity. Furthermore, the convergence properties of different solution strategies are analyzed. Monolithic and staggered solution schemes for the solution of the arising nonlinear discrete systems are studied in detail. To conclude, we demonstrate the versatility of the phase-field fracture approach in a real-world problem by comparing different simulations of conchoidal fracture using structured and unstructured meshes. K E Y W O R D Scrack driving force, crack propagation, multilevel methods, phase-field fracture INTRODUCTIONCrack growth is associated with the creation of new internal surfaces of unknown size and evolution. In the literature different possibilities for simulating crack propagation can be found. Besides the cohesive zone model, [1][2][3] the extended finite element methods [4,5] or eigenfracture strategies [6] which allow for modeling the crack as a sharp interface, diffuse interface approaches gain more and more attention. More precisely, the phase-field model is becoming very popular and constitutes a reliable way to predict the crack path. [7][8][9] During the last decades phase-field methods are used to describe a number of topics, that is, thermodynamics, [10] hydraulic fracture, that is, in porous media, [11][12][13][14] ductile materials, [15,16] anisotropy, [17][18][19][20] contact problems, [21] and many more. Most of the phase-field approaches are based on the minimization of the total potential energy that leads to a crack driving force corresponding to Griffith's energy release rate. [22] However, the approach requires a detailed consideration of the fact that only tensile states are responsible for crack growth. One popular way to take this into account is to decompose the strain energy function into a positive and negative part which correspond to the tensile and compressive parts, respectively. [8,9,23] This is not always physically meaningful. Thus, crack driving forces motivated by established fracture criteria have also been introduced. [24] Nevertheless, the phase-field model depends on a series of parameters which influence the results, like the location of crack initialization. In this work we will investigate the influences of these parameters in more detail. In particular, the phase-field This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Large scale simulation of pressure induced phase-field fracture propagation using Utopia

“…As it has been demonstrated, the RMTR method can achieve a speedup of factor 2-8, in terms of computational time, compared to widely used alternate minimization on standard benchmarks. In addition, the sensitivity of the method with respect to the choice of the model parameters, such as degradation function can be found in Bilgen et al (2019).…”

“…Miehe et al (2010bMiehe et al ( , 2010a enhanced the underlying mathematical model and introduced thermodynamically consistent, rate-independent formulation. Since then, the phase-field approach has become popular and it has been extended in many directions, including dynamic models (Bourdin et al 2011), generalization to large deformations (Hesch and Weinberg 2014;Bilgen et al 2019), adaptive fourth-order models (Goswami et al 2020), or anisotropic models for a fracture of fiber-reinforced matrix composites (Denli et al 2020). For further details, we refer the interested reader to the review provided in De Lorenzis et al (2020).…”

Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture

“…This gives rise to two convex minimization problems, which can be solved efficiently using standard solution strategies. Despite its robustness, the AM method exhibits slow convergence, which even deteriorates with increasing problem size [34]. Several approaches to accelerate the AM method have been proposed recently in the literature, e.g., over-relaxation strategies [35,36], stabilization techniques [37], or sub-stepping algorithms [38].…”

Large scale simulation of pressure induced phase-field fracture propagation using Utopia

“…Miehe et al [82,81] enhanced the underlying mathematical model and introduced thermodynamically consistent, rate-independent formulation. Since then, the phase-field approach has become popular in the literature and has been extended in many directions, including dynamic models [20,104], shells and plates approaches [6,2], generalization to large deformations [37,60,16], adaptive fourth-order models [50,115], hybrid schemes [50], or anisotropic models for a fracture of fiber-reinforced matrix composites [38]. Application of phase-field approaches to fracture initiation and propagation include also cohesive fractures [114,34] and hydraulic fracturing [15,85,56].…”