Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

The aim of the present paper is a systematic elaboration of a three dimensional finite element analysis tool for discontinuous fracture in brittle solids. Brittle or quasi-brittle fracture usually occurs when a material reaches the limit of its strength and no plastic deformation has been observed prior to failure. In the present approach, this kind of failure is characterized by three sets of governing equations: (i) the elastic bulk problem and (ii) the cohesive interface problem regarding the solid deformation field and (iii) the crack tracking problem concerning the crack kinematics. This manuscript describes a unique modular tool set for the coupled set of nonlinear equations. We focus in particular on the boundary conditions for the crack tracking problem of this analysis tool. We critically discuss important implementation details: (i) the choice of crack onset boundary conditions for the additional global field, (ii) the numerical integration, (iii) the modeling of geometrically exact crack tips for cohesive fracture, and (iv) the post-processing procedure for the discontinuity visualization. The potential of the method to simulate brittle fracture is demonstrated by qualitative and quantitative comparisons with experiments from the literature as well as by common benchmark problems.