Adaptive fourth-order phase-field modeling of ductile fracture using an isogeometric-meshfree approach

Abstract

The fourth-order phase-field modeling of ductile fracture in elastic–plastic materials is performed via an adaptive isogeometric-meshfree approach. In the developed phase-field model, the total energy functional consists of the elastic contribution and the dissipated contribution because of fracture and plasticity. The coupling of the plasticity to fracture is implemented by a degradation function that is applied to the elastic energy. The present fourth-order phase-field model is capable of relaxing the mesh size requirements while accurately regularizing sharp cracks. To further enhance the computational efficiency, the isogeometric-meshfree approach is adopted for the numerical implementation of the phase-field model within a staggered computational framework. The developed approach can flexibly implement the C1-continuity of a crack phase field that is required by the fourth-order model. Moreover, an adaptive mesh refinement strategy is developed, which includes the gradient-based refinement indicators and the field transfer operators. Numerical simulations of a series of representative cases show that the developed fourth-order model can accurately and efficiently capture complex ductile fracture patterns including plastic localization, crack initiation, propagation, and merging, which demonstrates the reliability of the adaptive fourth-order phase-field modeling of ductile fracture.