Implementation of the adaptive phase-field method with variable-node elements for cohesive fracture

In this paper, an adaptive phase-field model based on variable-node elements and error-indicator is presented to predict cohesive fracture evolution. The phase-field cohesive-zone model is characterized by the parameterized energetic degradation and crack geometric functions. A staggered iteration scheme is used to solve the coupled non-linear system of displacement field and phase field. The adaptive local refinement algorithm facilitated with error-indicator and variable-node elements is developed to improve computational efficiency. To determine the adaptive local refinement regions, we apply the phase-field threshold to characterize the crack regions and a novel history field threshold to denote crack tips. The variable-node elements are acted as transition elements to flexibly yet simply link the fine and coarse meshes. In addition, a fast method to generate the variable-node elements is given. Several representative numerical examples are studied to demonstrate the performance and accuracy of the proposed adaptive phase-field model, consisting of a mixed -model fracture of L-shape panel, the wedge-splitting test, the classic three point bending experiment and a plate with a hole and multi-cracks under tensile/shear loadings. The computer codes can be accessed at: https://github.com/hhuztc/Adaptive-PFM.git.