A physically consistent nonlocal multi‑scale damage model for quasi‑brittle materials with numerical simulation and experimental benchmarking

Abstract

In this study, a physically consistent nonlocal multi-scale damage model is proposed to characterize the fracture behavior of quasi-brittle materials under quasi-static and high-strain-rate loading scenarios. A strain-rate-dependent microstructural length scale and a stress-state-sensitive damage evolution law are integrated into the model to ensure mesh objectivity and stabilize the post-peak damage response. Through asymptotic homogenization, the evolution of microcracks is coupled with macroscopic stress fields, facilitating the physical consistency of multi-scale damage. Numerical implementation and experimental validation demonstrate the model’s capability to reproduce fracture characteristics under uniaxial compression. For the perforated prismatic specimen, the simulated peak stress reached 29.0 MPa, the critical strain was near 1.0 × 10⁻³, and crack growth up to 60 mm within 2.5 s. In mixed-mode fracture scenarios, the transition from tensile-shear to tensile-dominated failure is captured by the proposed model as flaw geometry varies. Under dynamic tensile scenarios, the critical transition from stable type I cracking to crack branching and type II-dominated failure at 1150 mm/s in the L-shaped specimen test. For this test at 2400 mm/s, the simulated peak load deviates by less than 2% from experimental measurements. Consistent crack morphologies across mesh resolutions further confirm the robustness, efficiency, and applicability of the proposed model in high-rate fracture simulations of quasi-brittle materials.