On the crack-driving force of phase-field models in linearized and finite elasticity

TL;DR

This paper examines the crack-driving force in phase-field models of fracture within linearized and finite elasticity, proposing generalized formulations that align better with fracture mechanics principles, supported by numerical examples.

Contribution

It introduces generalized variational formulations for the crack-driving force in phase-field fracture models, improving their consistency with fracture mechanics criteria.

Findings

Generalized formulations outperform traditional ones in numerical tests.

Ad-hoc driving forces can better capture crack propagation behavior.

The approach enhances the physical accuracy of phase-field fracture simulations.

Abstract

The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a variational crack-driving force. The definition of this force out of a tension-related energy functional does, however, not always agree with the established failure criteria of fracture mechanics. In this work different variational formulations for linear and finite elastic materials are discussed and ad-hoc driving forces are presented which are motivated by general fracture mechanical considerations. The superiority of the generalized approach is demonstrated by a series of numerical examples.