Crack opening calculation in phase-field modeling of fluid-filled fracture: A robust and efficient strain-based method

TL;DR

This paper introduces a new strain-based method for calculating crack opening in fluid-filled phase-field fractures, eliminating the need for complex post-processing algorithms and parameters, thus improving robustness and efficiency.

Contribution

The paper presents a novel, parameter-free, strain-based approach for crack opening calculation in phase-field models, enhancing accuracy and simplicity over existing methods.

Findings

Accurately computes crack opening without additional algorithms.

Works independently of element size and alignment.

Validated against analytical and numerical solutions.

Abstract

The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry poses a significant challenge in calculating the crack opening (aperture) of phase-field fracture, which governs the fracture permeability and hence the overall hydromechanical behavior. Although several approaches have been devised to compute the crack opening of phase-field fracture, they require a sophisticated algorithm for post-processing the phase-field values or an additional parameter sensitive to the element size and alignment. Here, we develop a novel method for calculating the crack opening of fluid-filled phase-field fracture, which enables one to obtain the crack opening without additional algorithms or parameters. We transform the displacement-jump-based kinematics of a fracture into a continuous strain-based version, insert it into a force balance equation on the fracture, and apply the phase-field approximation. Through this procedure, we obtain a simple equation for the crack opening which can be calculated with quantities at individual material points. We verify the proposed method with analytical and numerical solutions obtained based on discrete representations of fractures, demonstrating its capability to calculate the crack opening regardless of the element size or alignment.