Dual-State Peridynamic Contact Retrieval for Branching Cracks in Granite

Abstract

The accurate computational modeling of fracture mechanisms in heterogeneous brittle materials remains a formidable challenge in computational mechanics and geological engineering. Granite, characterized by its complex microstructural composition and inherent flaws, frequently exhibits intricate failure patterns including dynamic crack propagation, bifurcation, and extensive crack face contact under varying load conditions. Classical continuum mechanics formulations often struggle to capture these spontaneous discontinuities due to the spatial derivatives present in their governing equations. To overcome these limitations, the peridynamic theory, which utilizes integro-differential equations, has emerged as a robust alternative. This paper proposes a comprehensive dual-state peridynamic contact retrieval framework specifically designed to simulate branching cracks in granite. The dual-state approach introduces a novel algorithmic transition between cohesive bonding states and repulsive contact states, ensuring that newly formed crack surfaces do not unphysically interpenetrate during compressive wave reflections. By eliminating mathematical singularities at crack tips, the proposed framework autonomously captures crack initiation, propagation, and complex branching without requiring external criteria or guided enrichment functions. Extensive numerical investigations are conducted to evaluate the performance of the proposed algorithm under high strain rate dynamic loading. The results demonstrate that the dual-state contact retrieval mechanism significantly enhances the physical accuracy of the simulated fragmentation process, preserving the global energy balance while accurately resolving the interaction between secondary crack branches. This methodology provides a vital computational tool for predicting the mechanical response of granitic rock masses in applications ranging from deep geological repositories to enhanced geothermal systems.