Boundary element method: cells with embedded discontinuity modeling the fracture process zone in 3D failure analysis

Abstract

Damage and failure in quasi-brittle materials such as rocks, concrete, and ceramics, have a complex non-linear behavior due to their heterogeneous character and the development of a fracture process zone (FPZ), formed by micro-cracking around the tip of an induced or pre-existing flaw. A softening behavior is observed in the FPZ, and the linear elastic fracture mechanic (LEFM) cannot correctly reproduce the stress field ahead of the crack tip. The existence of the FPZ may be the intrinsic cause of the size effect. An appropriate modeling of this process zone is mandatory to reproduce accurately the failure propagation and consequently, the structural behavior. Different from most of the domain numerical techniques, the boundary element method (BEM) requires (besides the boundary division into elements) only the discretization of a small region where dissipative effects occur. Cells with embedded continuum strong discontinuity approach (CSDA), placed in the region where the crack is supposed to occur, are capable of capturing the transition of regimes in the failure zone. Numerical bifurcation analysis, based on the singularity of the localization tensor, is used to determine the end of the continuum regime. Weak and strong discontinuity regimes are associated with diffuse micro-cracks (strain discontinuity) and macro-crack (displacement discontinuity). A variable bandwidth model is used during the weak discontinuity regime to represent the advance of micro-cracks density and their coalescence. Continuum and discrete cohesive isotropic damage models are used to describe the softening behavior. Analysis of three-dimensional problems with single crack in standard and mixed fracture modes, using this transitional approach and the BEM cells is firstly presented in this work. Experimental reference results are used to attest the capability of the approach in reproducing the structural behavior during crack propagation. Some necessary advances required for its applications for general complex structural problems are pointed out.