A novel singular ES-FEM for crack growth simulation

Abstract

A novel singular seven-node crack-tip triangular element with edge-based strain smoothing is formulated for modeling crack growth in solids. The present singular ES-FEM method uses a basic mesh of linear triangular elements and a special layer of seven-noded crack-tip elements connected to the crack-tip. The seven-noded crack-tip element has two additional nodes on each of the edges connected to the crack-tip, allowing efficient enrichment of the displacement field near the crack-tip without loss of partitions-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. For crack propagation simulation, the Delaunay triangulation procedure associated with the Laplacian smoothing technique is used to automatically generate meshes. Several benchmark problems are used to show the accuracy and robustness of the proposed method.