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

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.

39 pages, 21 figures

References in corpus (3)

• Dynamic instabilities of fracture under biaxial strain using a phase field model
• High-accuracy phase-field models for brittle fracture based on a new family of degradation functions
• Fracture surfaces of heterogeneous materials: a 2D solvable model

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• An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method
• Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation
• A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture
• A spatially adaptive phase-field model of fracture
• Dynamic phase-field fracture with a first-order discontinuous Galerkin method for elastic waves