Development of efficient numerical methods for the phase field model

Abstract

Various numerical methods for fracture analysis have been proposed, but they faced limitations due to several problems, and a new phase field model was recently proposed. However, it requires a high computational cost due to the rapid increase in degrees of freedom caused by the fine mesh near the crack tip and due to iterative solution procedure such as the Newton-Raphson method. Although various adaptive mesh refinement schemes have been applied to the phase field model, improvement of the computational efficiency still remains a problem to be solved. In this dissertation, new numerical methods to improve the computational efficiency of the phase field model for brittle fracture are proposed. First, in order to reduce the computation time, an adaptive update scheme is proposed. The whole domain is divided into the domain around the crack tip and the rest domain. By frequently updating the structural properties of the domain around the crack tip and occasionally updating the structural properties of the remaining domain, the computational efficiency is improved. For further efficiency improvement, the adaptive mesh refinement scheme using variable-node finite elements is applied. The proposed method shows that the computational cost is greatly reduced through various numerical examples. In addition, mesh coarsening using the phantom-node method is also proposed. The fine mesh in the domain where the crack tip has already passed is replaced by the coarse mesh to which the phantom-node method is applied, which drastically reduces the degrees of freedom. The performance of the proposed method is verified through several numerical examples. It is expected that the proposed methods will be effectively utilized for fracture analysis using the phase field model.