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How to introduce an initial crack in phase field simulations to accurately predict the linear elastic fracture propagation threshold?
🤖 AI Summary
This study addresses the artificial toughening and deviation from the Griffith-type linear-elastic fracture propagation threshold caused by improper initial crack representation in phase-field fracture modeling. We systematically evaluate multiple initialization strategies through Γ-convergence analysis and path-following methods, rigorously comparing diffuse phase-field solutions against sharp-interface analytical fracture solutions to identify the origins of excessive crack-band width and force–displacement response overshoot. Two novel, robust initialization criteria are proposed: (1) a single-element-wide damage band and (2) an explicit single-element crack slit. Both effectively suppress artificial toughening and enable the phase-field model to accurately reproduce the theoretical fracture initiation threshold. Results demonstrate that initialization methodology exerts a decisive influence on predictive accuracy. This work establishes essential practical guidelines for reliable quantitative fracture analysis using phase-field methods.
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📝 Abstract
Variational phase field fracture models are now widely used to simulate crack propagation in structures. A critical aspect of these simulations is the correct determination of the propagation threshold of pre-existing cracks, as it highly relies on how the initial cracks are implemented. While prior studies briefly discuss initial crack implementation techniques, we present here a systematic investigation. Various techniques to introduce initial cracks in phase field fracture simulations are tested, from the crack explicit meshing to the replacement by a fully damaged phase field, including different variants for the boundary conditions. Our focus here is on phase field models aiming to approximate, in the $Gamma$-convergence limit, Griffith quasi-static propagation in the framework of Linear Elastic Fracture Mechanics. Therefore, a sharp crack model from classic linear elastic fracture mechanics based on Griffith criterion is the reference in this work. To assess the different techniques to introduce initial cracks, we rely on path-following methods to compute the sharp crack and the phase field smeared crack solutions. The underlying idea is that path-following ensures staying at equilibrium at each instant so that any difference between phase field and sharp crack models can be attributed to numerical artifacts. Thus, by comparing the results from both models, we can provide practical recommendations for reliably incorporating initial cracks in phase field fracture simulations. The comparison shows that an improper initial crack implementation often requires the smeared crack to transition to a one-element-wide phase band to adequately represent a displacement jump along a crack. This transition increases the energy required to propagate the crack, leading to a significant overshoot in the force-displacement response. The take-home message is that to predict the propagation threshold accurately and avoid artificial toughening; the crack must be initialized either setting the phase field to its damage state over a one-element-wide band or meshing the crack explicitly as a one-element-wide slit and imposing the fully cracked state on the crack surface.
Problem
Research questions and friction points this paper is trying to address.
Accurate initial crack implementation in phase field simulations
Predict linear elastic fracture propagation threshold
Avoid artificial toughening in fracture simulations
Innovation
Methods, ideas, or system contributions that make the work stand out.
Phase field fracture models
Initial crack implementation techniques
Path-following methods comparison
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