A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials

This paper presents a framework for r-adaptive quasi-static configurational force (CF) brittle crack propagation, cast within a discontinuous Galerkin (DG) symmetric interior penalty (SIPG) finite element scheme. Cracks are propagated in discrete steps, with a staggered algorithm, along element interfaces, which align themselves with the predicted crack propagation direction. The key novelty of the work is the exploitation of the DG face stiffness terms existing along element interfaces to propagate a crack in a mesh-independent r-adaptive quasi-static fashion, driven by the CF at the crack tip. This adds no new degrees of freedom to the data structure. Additionally, as DG methods have element-specific degrees of freedom, a geometry-driven p-adaptive algorithm is also easily included allowing for more accurate solutions of the CF on a moving crack front. Further, for nondeterminant systems, we introduce an average boundary condition that restrains rigid body motion leading to a determinant system. To the authors' knowledge, this is the first time that such a boundary condition has been described. The proposed formulation is validated against single and multiple crack problems with single- and mixed-mode cracks, demonstrating the predictive capabilities of the method.