Pervasive cracking of heterogeneous brittle materials using a multi-directional smeared crack band model

A numerical methodology is presented for the plane stress analysis of pervasive cracking in heterogeneous materials. The smeared crack band concept is used in conjunction with the multi-directional crack model to objectively model cracking in a finite element analysis while allowing cracks to form at different orientations. The multi-directional crack approach is able to reduce stress-locking behavior that plagues conventional fixed crack models. An advanced meshing technique is used to generate meshes with smooth grain boundaries and high-quality elements of uniform size. The sequentially linear analysis procedure is used in place of an iterative method to avoid instability issues and to capture the snap-type behavior of brittle materials. The implementation is generalized to allow for the analyses of heterogeneous materials composed of anisotropic constituents; furthermore, elastic stiffnesses and fracture parameters of the materials studied can vary with orientation. The proposed methodology is used to study cracking in a concrete microstructure obtained using X-ray computed tomography. Bulk constitutive behavior and crack patterns are compared with results of other crack methods in the literature. The proposed methodology is also used to analyze cracking within a computer-generated polycrystalline microstructure composed of Voronoi-like grains with the properties of alumina. Using the capabilities of the proposed methodology, a comparative study is performed by varying the tensile strengths along grain boundaries relative to their interiors. (C) 2017 Elsevier Ltd. All rights reserved.