Simulation of compaction and crushing of concrete in ballistic impact with a new damage model

Although many aspects of the fracturing process of concrete are now well understood and successfully simulated with various models, it is still very difficult to properly simulate the different failure mechanisms observed in a concrete structure induced by ballistic impact. In this paper, an enhanced version of the effective-rate-dependent nonlocal damage model [Eng. Fracture Mechanics, 176 (2017)] is proposed to simulate the response of concrete in such events. Hydrostatic damage has been added to the formulation in order to take the damage of the material matrix observed while porosity reduces during compaction into account. Besides controlling the evolution of the nonlinear volumetric response of the material, this new damage variable contributes to the deterioration of the material stiffness upon confinement. It is demonstrated that the description of the nonlinear volumetric response of concrete by an equation of state (EOS) as a plasticity phenomenon, as it is commonly done in hydrodynamic constitutive modeling, is unrealistic for concrete. Such formulations fail to represent the effect of the loss of cohesion observed during compaction on the deviatoric response of the material. By taking this phenomenon into consideration, the proposed model systematically predicts the relevant failure modes (cratering, tunneling, radial cracking and spalling) observed during ballistic impact on a concrete plate as a function of the projectile velocity and plate thickness.