A phase-field cohesive fracture model free from the length scale constraints

Abstract

In conventional phase-field cohesive fracture methods, an upper bound on the phase-field length scale parameter is typically imposed to ensure the convexity of the energy degradation function. However, this constraint can result in substantial computational costs when analyzing large-scale structures, geological fractures, or fractures in high-strength materials. To overcome this limitation, this work introduces a novel field variable that guarantees the convexity of the energy degradation function is always satisfied, thereby eliminating the physical constraint on the phase-field length scale parameter. Based on this innovation, a new class of phase-field cohesive fracture models is formulated using a variational approach, and the intrinsic relationship between the characteristic function and the cohesive law is established through the one-dimensional analytical solution. Both implicit and explicit dynamic algorithms are developed for the numerical implementation of the model. The effectiveness and robustness of the proposed approach are demonstrated through simulations of several typical fracture problems. The results indicate that the model can efficiently and accurately address large-scale fracture and high-strength material failure analyses, while maintaining insensitivity to the phase-field length scale parameter in both static and dynamic cases. These findings highlight the model’s potential for broad application in the computational analysis of complex fracture phenomena.