S-FEM FOR FRACTURE PROBLEMS, THEORY, FORMULATION AND APPLICATION

Abstract

This paper briefs some of recent works on applications of the smoothed finite element method (SFEM) to fracture problems. In the SFEM formulation for simulating the singular filed near the crack-tip, it is known that one can directly enrich the filed by adding in proper terms needed to simulate the singularity, which can be done in a number of ways (see the SFEM book). In this work a generalized technique called the "enriched linear PIM" for constructing shape functions is used to formulate a special "five-node (T5) singular crack-tip element" that can produce a proper order of stress singularity near the crack-tip. One layer of T5 crack-tip singular elements are used in a basic mesh of linear elements leading to a very simple model that can be crated automatically for complicated geometry. Because the SFEM uses weakened weak formulations, such a simple model does not require transition elements and the compatibility is ensured. In addition, the singular terms of functions as well as mapping procedures are no longer necessary to compute the stiffness matrix. Thus, the singular SFEM method is straightforward and can be easily implemented in the existing codes. The stress intensity factors of mix-modes can also be easily evaluated by an appropriate treatment during the domain form of the interaction integral, due to the use of simple triangular mesh. The effectiveness of the present singular T5 element is demonstrated via benchmark examples.