Abstract
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In the phase-field framework, the surface energy associated with crack formation is calculated by evaluating a functional defined in terms of a scalar order parameter and its gradients. These in turn describe the fractures in a diffuse sense following a prescribed regularization length scale. Imposing stationarity of the total energy leads to a coupled system of partial differential equations that enforce stress equilibrium and govern phase-field evolution. These equations are coupled through an energy degradation function that models the loss of stiffness in the bulk material as it undergoes damage. In the present work, we introduce a new parametric family of degradation functions aimed at increasing the accuracy of phase-field models in predicting critical loads associated with crack nucleation as well as the propagation of existing fractures. An additional goal is the preservation of linear elastic response in the bulk material prior to fracture. Through the analysis of several numerical examples, we demonstrate the superiority of the proposed family of functions to the classical quadratic degradation function that is used most often in the literature.
Highlights
The accurate simulation of fracture evolution in solids is a major challenge for computational algorithms, in large part due to crack paths that are generally unknown a priori
Enthusiasm in the relatively new phase-field paradigm has led to its application in a number of diverse problems, which include cracking in piezoelectric solids (Miehe et al, 2010b), fluid-driven fracture propagation (Miehe et al, 2015b; Mikelicet al., 2015), thermal shock-induced cracks (Bourdin et al, 2014) and fragmentation of battery electrode particles (Miehe et al, 2015a)
We look at two quantities of interest: the energy release rate at the crack tip represented by the J-integral, and the length of crack extension described by the phase-field that is obtained by evaluating the functional (φ) =
Summary
The accurate simulation of fracture evolution in solids is a major challenge for computational algorithms, in large part due to crack paths that are generally unknown a priori. We introduce a new family of degradation functions that allows for correctly reproducing the onset of failure for reasonably chosen arbitrary values of the regularization parameter The latter point is important since the problem of regularization-dependent material response is not solved in the alternative formulations previously mentioned, and is confined to brittle fracture as demonstrated in the numerical results of Areias et al (2016) on cracking in elastoplastic materials. Enthusiasm in the relatively new phase-field paradigm has led to its application in a number of diverse problems, which include cracking in piezoelectric solids (Miehe et al, 2010b), fluid-driven fracture propagation (Miehe et al, 2015b; Mikelicet al., 2015), thermal shock-induced cracks (Bourdin et al, 2014) and fragmentation of battery electrode particles (Miehe et al, 2015a) This underscores the need for quantitative accuracy with regard to the fracture model, in the case of crack nucleation that is often the critical failure mechanism for many such applications.
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