A strain-rate-dependent bond-based peridynamic model for dynamic fracture

A rate-dependent constitutive formulation is developed within the bond-based peridynamic (BB-PD) framework for modeling dynamic fracture in quasi-brittle materials. A nonlinear strain-rate-dependent micromodulus is introduced to capture dynamic stiffening, while an exponential softening law describes progressive bond degradation and the associated energy dissipation. The bond deformation is decomposed into normal and tangential components to account for both tensile and shear deformation, and an equivalent bond stretch is employed to characterize the onset and evolution of bond failure. By incorporating the coupled effects of strain-rate sensitivity and inertia, the critical failure stretch is derived from an energy-equivalence condition between the bond-level fracture energy and the macroscopic fracture energy. This formulation provides a physically consistent relationship among rate-dependent stiffness, fracture toughness, and dynamic effects without introducing independent empirical failure parameters. Comprehensive numerical studies using benchmark dynamic-fracture problems demonstrate that the proposed model accurately reproduces fracture patterns, crack propagation velocities, and energy evolution over a broad range of loading rates, in close agreement with available experimental and theoretical results. Application to high-velocity projectile impact on ice further reveals a strain-rate-controlled transition in fracture mechanisms, from predominantly back-face tensile cracking at relatively low strain rates to through-thickness shear failure accompanied by localized crushing at high strain rates. The proposed formulation provides a unified, physically motivated, and computationally efficient framework for modeling high-strain-rate fracture in quasi-brittle materials.