An adaptive dynamic phase-field method using the variable-node elements for cohesive dynamic fracture

This work presents an adaptive phase-field method incorporated into a finite element framework combined with variable-node elements to investigate the cohesive dynamic fracture. The proposed framework builds upon the regularized phase-field cohesive-zone model as its foundation utilizes a hybrid form of the history field to drive the crack evolution. A staggered iteration scheme is utilized to compute the displacement and phase-field variables for the coupled elastic-phase field system. The error indicator, utilizing the phase-field as well as the history strain variables, is employed to control the adaptive refinement process. The variable-node element technique facilitates adaptive mesh refinement, which is simple and flexible to act as a transition element between coarse and refined elements. In addition, an implicit HHT time integration scheme is employed for temporal discretization. Several standard problems are presented to showcase the efficiency and accuracy of the proposed method, highlighting its superiority when compared to the results documented in the literature. The results show that the proposed framework can significantly improve computational efficiency without affecting the accuracy of numerical results.