A multi-constitutive four-dimensional lattice spring model for high-velocity penetration of metallic projectiles into rock-like targets

High-velocity penetration of kinetic projectiles into brittle targets (rock and concrete) involves coupled large deformation, fragmentation, and damage evolution. To simulate these coupled responses within a unified framework, a multi-constitutive four-dimensional lattice spring model (4D-LSM) is developed. Johnson-Holmquist-Beissel (JHB) model is adopted to describe the pressure-dependent strength, damage and fragmentation of rock and concrete. A modified Johnson-Cook (MJC) model is proposed for metallic projectiles by incorporating damage-dependent strength and shear-stiffness degradation, residual strength-based thermal softening, and incremental damage evolution. The resulting coupled framework, termed MJC-JHB-4DLSM, integrates the two constitutive models through a unified explicit stress-update procedure. The MJC formulation is independently validated against Taylor impact tests, reproducing the axial shortening, radial expansion, and progressive failure of metallic rods under high strain-rate loading. The coupled framework is further assessed through hypervelocity penetration of long rods into concrete and granite targets. Typical crater–tunnel and crater-dominated failure modes, projectile erosion, and penetration-regime transitions are successfully reproduced. The predicted penetration depth and residual projectile response show reasonable agreement with experimental observations. Simulations of oblique penetration into multilayer spaced concrete targets further capture the progressive accumulation of projectile attitude perturbation and trajectory deviation. The proposed framework provides a unified continuous-discontinuous approach for analysing high-velocity penetration into rock-like targets, with potential applications to the design and safety assessment of underground protective structures.