A NOVEL GENERAL FORMULATION FOR SINGULAR STRESS FIELD USING THE ES-FEM METHOD FOR THE ANALYSIS OF MIXED-MODE CRACKS

This paper presents a general formulation for simulating the singular stress field at the vicinity of the crack-tip for linear fracture mechanics problems, based on the edge-based smoothed finite element method (ES-FEM) settings. This novel "singular ES-FEM" makes use of the unique feature offered by the ES-FEM that only the assumed displacement values (not the derivatives) are required to compute the stiffness matrix of the discretized system. The present singular ES-FEM method uses a basic mesh of linear triangular elements and a layer of novel "five-noded crack-tip elements" sharing the crack-tip node. The five-noded crack-tip element has one additional node on each of the edges connected to the crack-tip, and the locations of the "edge-node" can be arbitrary. A number of examples are analyzed and the results demonstrate that the present singular ES-FEM is generally softer and much more accurate than the existing FEM. The stress intensity factors obtained using the singular ES-FEM are very stable for d...