Orientation-Dependent Degradation for Anisotropic Phase-Field Fracture
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The phase-field method has emerged as a powerful computational framework for fracture mechanics, offering a robust and physically consistent description of crack initiation and propagation grounded in Griffith’s criterion [1]. A wide variety of formulations have been proposed, mainly differing in the analytical expressions adopted for the degradation and dissipation functions [2,3]. These differences reflect the ongoing effort to improve both the accuracy and physical interpretability of phase-field fracture models. In previous works, novel semi-empirical models were developed [4] by reformulating the phase-field approach for brittle fracture with particular emphasis on the degradation function, which was obtained from the homogenization of evolving microstructures containing voids. In the present contribution, this framework is further extended by introducing additional microstructural variables to represent more complex void geometries and their orientation within the microstructure. This enrichment enables the formulation of anisotropic phase-field models based solely on the definition of the degradation function, in contrast to existing approaches that primarily rely on modifications of the dissipation term or the introduction of additional damage variables [5,6]. Moreover, the incorporation of orientation information enhances the prediction of macroscale crack paths while allowing their resolution with fewer finite elements, thereby reducing the computational cost typically associated with phase-field simulations.
