A phase-field modeling method for the mixed-mode fracture of brittle materials based on spectral decomposition

Abstract

The phase-field method is artful to handle sharp crack discontinuities by regularizing the sharp crack surface topology with a function. In the phase-field theory, the phase field characterizing the crack is driven by the strain energy. The strain energy of the crack-driving part is the key to simulate the realistic crack surface. In this study, a new framework of the phase-field method is proposed based on the unified tensile fracture criterion, in which the crack-driving strain energy is evaluated by the spectral representation with a thermodynamic consistent projection operator to ensure the thermodynamic consistency. The mixed-mode fracture of brittle materials can be well simulated. Furthermore, a new degradation function is proposed to simulate the brittle materials with different degradation rates. The proposed phase-field modeling method is implemented by a staggered algorithm, in which the phase field and displacement field are successively solved and updated by the subroutines UEL and UMAT of the commercial finite element software ABAQUS. The comparison with experimental data shows that the proposed phase-field modeling method can quantitatively and qualitatively simulate both the cracking and mechanical behavior of mixed-mode fracture.