A computational framework of three-dimensional configurational-force-driven brittle crack propagation

Abstract

We consider a variational formulation of quasi-static brittle fracture and develop a new finite-element-based computational framework for propagation of cracks in three-dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius–Planck inequality in the sense of Coleman’s method. Consequently, the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces. Therefore, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. In a consistent way with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh. The crucial step for the success of this procedure is its embedding into an r-adaptive crack-facet reorientation procedure based on configurational-force-based indicators in conjunction with crack front constraints. We propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems with successively decreasing overall stiffness, providing a robust algorithmic setting in the postcritical range. The predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations.