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 elab1 oration of a three dimensional finite element analysis tool for 2 discontinuous fracture in brittle solids. Brittle or quasi-brittle 3 fracture usually occurs when a material reaches the limit of its 4 strength and no plastic deformation has been observed prior 5 to failure. In the present approach, this kind of failure is char6 acterized by three sets of governing equations: (i) the elastic 7 bulk problem and (ii) the cohesive interface problem regard8 ing the solid deformation field and (iii) the crack tracking 9 problem concerning the crack kinematics. This manuscript 10 describes a unique modular tool set for the coupled set of 11 nonlinear equations. We focus in particular on the boundary 12 conditions for the crack tracking problem of this analysis 13 tool. We critically discuss important implementation details: 14 (i) the choice of crack onset boundary conditions for the 15 additional global field, (ii) the numerical integration, (iii) the 16 modeling of geometrically exact crack tips for cohesive frac17 ture, and (iv) the post-processing procedure for the disconti18 nuity visualization. The potential of the method to simulate 19 brittle fracture is demonstrated by qualitative and quantita20 tive comparisons with experiments from the literature as well 21 as by common benchmark problems. 22 P. Jäger Department of Mechanical Engineering, University of Kaiserslautern, 67653 Kaiserslautern, Germany e-mail: [email protected] P. Steinmann (B) Department of Mechanical Engineering, Friedrich-Alexander University Erlangen-Nuremberg, 91058 Erlangen, Germany e-mail: [email protected] E. Kuhl Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA e-mail: [email protected]