The Splitting Method and the GFEMin the Two-Dimensional Analysis of Linear Elastic Domains with Multiple Cracks

The aim of this paper is to analyse two-dimensional linear elastic continuum containing multiple interacting cracks. Both the mechanical model and the numerical approach are addressed throughout the text as key concepts for the computational framework, whose main characteristics will be described. The Splitting Method is a decomposition method considered for mechanical modeling of multiple interacting cracks. Accordingly, the original problem is divided into a set of global and local sub-problems. The Generalized Finite Element Method (GFEM) is adopted aiming at finding accurate numerical solutions for local sub-problems. Such problems are conceived so as to consider the stress concentration and the effects of interaction on the cracks. The main findings are related to the effectiveness of the proposed combination between the Splitting Method and the GFEM to provide accurate results, as well as the versatility of the conceived computational framework for analyzing different scenarios, including cracks of multilinear shapes and mixed mode fractures. Finally, it is possible to verify that the GFEM provides precise results using simpler meshes, in comparison with standard FEM used, for example in Franc2D (R).