A phase-field formulation for dynamic cohesive fracture

Abstract

We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress-strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro-and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.

Comparison of peridynamic and phase-field models for dynamic brittle fracture in glassy materials

“…For the quasi-static case, other forms of degradation functions in PFM have been recently proposed to increase the accuracy in predicting the critical loads associated with crack nucleation and preserving the linear elastic response in the bulk material prior to fracture [94]. These degradation functions avoid a noticeable localization of the phase field before the nucleation of a crack [95][96][97] or approximate a cohesive-type response for materials that exhibit some ductility after reaching their ultimate strength [98]. We have not investigated whether these newer PF models improve upon the results shown here.…”

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

“…There have been several recent efforts emphasizing the requirement of a generalized cohesive description of fracture using the phase field method [250,251], see, also Lorentz [252]. More specifically, Wu and Nguyen [251] proposed a unified phase field theory, namely the PF-CZM, for brittle and quasi-brittle fractures which converges to a cohesive zone model within the limits of a vanishing length-scale parameter.…”

“…PF-CZM was compared to the XFEM in [253] and further extended to the case of dynamic fracture in [254]. Furthermore, Geelen et al [250] extended the work introduced in [255] to a dynamic cohesive fracture model incorporating phase field formulations.…”

“…Higher values of the length-scale parameter lead to lower peak forces and vice versa. In recent formulations, see, e.g., Wu and Nguyen [251] and Geelen et al [250] this is alleviated, hence providing a significant advantage in enhancing the critical-stress predicting capabilities of the phase field method. In Miehe et al [256], generalized crack-driving forces with a failure criteria based on the maximum principal stress were introduced which also succeeded in predicting critical fracture loads unaffected by the length-scale parameter.…”

Considerations on a phase‐field model for adhesive fracture

“…To avoid using an auxiliary field, level set methods have also been utilized . Other approaches, which set out to model cohesive fracture rather exploit the variational phase‐field approach to brittle fracture and attempt to obtain a cohesive‐like fracture behavior by modifying the assumed phase‐field distribution perpendicular to the center of the crack, the degradation function, or attempt to reconstruct the crack opening from the phase field …”