Improvement on six-node triangular finite element (IT6) using twice-interpolation strategy for linear elastic fracture mechanics

Abstract

An improved six-node triangular finite element based on a twice-interpolation strategy (TIS) for accurately modeling singular stress fields near crack tips of two-dimensional (2D) cracks in solids is presented. In contrast to the traditional approaches, the approximation functions constructed based on the TIS involve both nodal values and averaged nodal gradients. The main idea of applying the TIS is to make the trial solution and its derivatives continuous across inter-element boundaries, or in other words, stresses can be smoothly transited element by element. This could improve the accuracy of the computed gradients of the trial solution and avoid tackling the smoothing operation technique generally utilized during the post-processing process. Another important issue should be noted that the TIS does not increase the total number of the degrees of freedom (DOFs) of the whole system. It implies that the total number of DOFs discretized by the proposed element is the same as that by the standard FEM. The stress intensity factors (SIFs) are estimated using the proposed method. The accuracy and efficiency of the proposed element are verified by some numerical examples.