On singular ES-FEM for fracture analysis of solids with singular stress fields of arbitrary order

The singular edge-based smoothed finite element method (sES-FEM) using triangular (T3) mesh with a special layer of five-noded singular elements (sT5) connected to the singular point, was proposed to model fracture problems in solids. This paper aims to extend the previous studies on singular fields of any order from −0.5 to 0, by developing an analytical means for integration to obtain the smoothed strains. We provide a more efficient practical formulae to estimate the stress intensity factor(SIF) for singular fields of mentioned order. The sT5 element has an additional node at each of the two edges connected to the crack tip, and the displacements are enriched with necessary terms to simulate the singularity. A weakened weak (W2) formulation is used to avoid the differentiation to the assumed displacement functions. The stiffness matrix is computed by using the smoothed strains calculated analytically from the enriched shape functions. Furthermore, our analytical integration techniques reduces the dependency on the order of numerical integration during the computation of the smoothed strain matrix. Several examples have been presented to demonstrate the reliability of the proposed method, excellent agreement between numerical results and reference observations shows that sES-FEM is an efficient numerical tool for predicting the SIF for singular fields.