Adaptive finite element method for hybrid phase-field modeling of three-dimensional cracks

Phase-field modeling of cracks in three dimensions (3D) is challenging due to expensive computational efforts caused by inefficient solution of non-linear governing equations as well as the requirement of extremely fine mesh for crack resolution. In this paper, a combination technique aiming at these two issues is presented. Firstly, a hybrid phase-field model is implemented in 3D with a simple and robust one-pass staggered solution scheme, yielding a linear system of governing equations which can be solved efficiently. Secondly, adaptive mesh refinement using the predictor-corrector algorithm is developed such that this hybrid model can be solved with minimal number of nodes. Numerical results show that computational cost of 3D phase-field modeling is dramatically reduced and complex crack events including initiation, mixed mode propagation, non-planar extension and twisting can be efficiently modeled with preferable robustness. Perfect agreement between numerical and experimental results on crack paths and application of the proposed method to the fracture of complicated engineering structures are demonstrated.

Automated summary

This paper presents a combination technique to address the computational cost and high crack resolution requirements in three-dimensional phase-field modeling of cracks. The technique utilizes a simple and robust one-pass staggered solution scheme to implement a hybrid phase-field model, and incorporates adaptive mesh refinement using the predictor-corrector algorithm to minimize the number of nodes. The results show a significant reduction in computational cost and efficient modeling of complex crack events.