A generalized phase-field cohesive zone model ($\mu$PF-CZM) for fracture

TL;DR

This paper introduces a generalized phase-field cohesive zone model ($$PF-CZM) that broadens the scope of fracture modeling by incorporating an extra dissipation function, enabling accurate simulation of brittle and cohesive fractures with various softening behaviors.

Contribution

The paper presents a new $$PF-CZM that analytically determines characteristic functions for universal fracture modeling, handling complex traction-separation laws and ensuring insensitivity to key parameters.

Findings

Global fracture responses are insensitive to phase-field length scale and traction order parameter.

The model can handle both concave softening and high-order cohesive traction behaviors.

Numerical examples validate the model's ability to simulate brittle and cohesive fractures accurately.

Abstract

In this work a generalized phase-field cohesive zone model ($\mu$PF-CZM) is proposed within the framework of the unified phase-field theory for brittle and cohesive fracture. With the introduction of an extra dissipation function for the crack driving force, in addition to the geometric function for the phase-field regularization and the degradation function for the constitutive relation, theoretical and application scopes of the original PF-CZM are broadened greatly. These characteristic functions are analytically determined from the conditions for the length scale insensitivity and a non-shrinking crack band in a universal, optimal and rationalized manner, for almost any specific traction-separation law. In particular, with an optimal geometric function, the crack irreversibility can be considered without affecting the target traction-separation softening law. Not only concave softening behavior but also high-order cohesive traction, both being limitations of the previous works, can be properly dealt with. The global fracture responses are insensitive not only to the phase-field length scale but also to the traction order parameter, though the crack bandwidth might be affected by both. Despite the loss of variational consistency in general cases, the resulting $\mu$PF-CZM is still thermodynamically consistent. Moreover, the existing numerical implementation can be adopted straightforwardly with minor modifications. Representative numerical examples are presented to validate the proposed $\mu$PF-CZM and to demonstrate its capabilities in capturing brittle and cohesive fracture with general softening behavior. The insensitivity to both the phase-field length scale and the traction order parameter is also sufficiently verified.