Rate-dependent constitutive modelling of dynamic fracture in quasi-brittle materials

The dynamic fracture of quasi-brittle materials, including rocks and concrete, is characterised by highly inhomogeneous deformation along localised cracking paths, exhibiting a significant rate-dependent effect that governs both fracture toughness and crack propagation trajectories. To capture the significant discontinuities of the localised fracturing band and its rate-dependent failure mechanisms, this study proposes a novel rate-dependent cohesive model integrated within a double-scale constitutive framework. The framework incorporates the localised failure mechanism as an intrinsic characteristic by using kinematic enrichment to account for the high deformation gradient across the localisation band. The proposed rate-dependent cohesive model distinctly incorporates the Dynamic Increase Factors (DIF) for both tensile and shear strength components to characterise mixed-mode dynamic fracture behaviour. Furthermore, by featuring a length scale intrinsically linked to the volume element size at the constitutive level, the size effects is naturally incorporated. The model's performance and promising features are demonstrated through its ability to capture dynamic fracture initiation, orientation and propagation under various impact load conditions. This opens the potential for understanding and simulating the complex dynamic fracture processes in quasi-brittle materials under high strain rate conditions, offering valuable insights for engineering applications involving impact load and dynamic structural integrity.