High-accuracy phase-field models for brittle fracture based on a new family of degradation functions

By J. M. Sargado, Eirik Keilegavlen, Inga Berre, Jan Martin Nordbotten Department of Mathematics, University of Bergen Christian Michelsen Research Department Civil, Environmental Engineering, P. University.. 2017

207 citations recorded by the source corpus.

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.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0d9e642e3229815becbd337ebf639fc83728376c

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In Mechanics of Materials

Citations in the corpus

A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics (2018, background): “Here we follow the terminology in [76] which refers to a brutal crack propagation as the crack growth that occurs while dissipation increases rapidly and leads to a sudden dip in total free energy.”
Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion (2020, methodology): “The prescribed phase-field value was shown to be necessary as the creation of the crack required more energy than the propagation of an already existing damage field (Klinsmann et al., 2015; Sargado et al., 2018; Tanné et al., 2018).”