FEM-BEM superposition method for fracture analysis of quasi-brittle structures

Abstract

Fracture analysis of civil engineering structures often requires appropriate modeling of discrete cracks propagating in an inhomogeneous or nonlinear material. For example, quasi-brittle materials, such as concrete, are characterized by formation of cracks with fracture process zone under tension and plasticity under compression. Application of either finite element method (FEM) or boundary element method (BEM) to problems involving simultaneously discrete cracks and inhomogeneities or plastic deformations faces certain difficulties. Therefore, we propose the FEM-BEM superposition method, which removes the respective methods disadvantages while keeping their advantages. In the proposed method, the original problem involving both material inhomogeneity or plasticity and discrete cracks is decomposed into two subproblems. The inhomogeneity or inelastic deformation is represented in only one of the subproblems, while the cracks appear only in the other. The former subproblem is analyzed using FEM and the latter one by BEM, so as to utilize the advantages of the two methods. The solution of the original problem is then obtained by superposing the solutions of the two subproblems. In order to verify validity of the proposed method we present numerical results of several examples, including both linear-elastic and nonlinear fracture mechanics. The results are compared with available analytical solutions or with data computed by other numerical methods, showing both accuracy and computational superiority of the proposed method.