A damage-driven adaptive radial point interpolation method for phase field model of brittle fracture

Abstract

To enhance the computational accuracy and efficiency in the analysis of phase field model (PFM) for brittle fracture, a damage-driven adaptive Radial Point Interpolation Method (DARPIM) is proposed. We employ the Polyharmonic Spline (PHS) radial basis function augmented with linear polynomial basis to approximate the displacement field as well as phase field. The coupled non-linear system of these two fields is solved by the staggered iteration scheme. Motivated by the damage evolution principle of continuum damage mechanics, we design a novel refinement criterion to improve both computational efficiency and accuracy of RPIM. In this criterion, the smeared crack zone is divided into low-, medium-, and high-damage regions based on the phase field value, and the corresponding refinement factor in each region is taken as 0.5, 1, and 2, respectively. The significant advantage of this criterion is that it can not only automatically refine nodes by tracking the crack evolution process, but also continuously adjust node density from sparse to dense within the smeared crack zone. To evaluate the accuracy, efficiency and robustness of the DARPIM, several 2D and 3D examples are simulated. The results demonstrate that the proposed method can capture the true crack paths with considerably fewer nodes, while the crack propagation paths and load–displacement curves exhibit excellent agreement with experimental data and results reported in the published literature.