A note on the dynamic spherical cavity expansion of concrete with liquid constitutive model

High pressure is applied to concrete target by the projectile in hypervelocity penetration. Moreover, concrete material which undergoes large deformation is incompressible and can be depicted by liquid constitutive model. The present work modifies the cavity expansion theory by characterizing the incompressibility with Bingham liquid constitutive model considering the viscosity of the incompressible material according to Cleja-Tigoiu's work. The analytic expression for the relationship between the pressure on the cavity boundary and the velocity of the cavity expansion is derived in this paper. Then, the effects of material parameters in the modified model are studied, which is the basis of the calculation of the drag force in hypervelocity penetration. At last, some penetration depth results of long rod impact concrete target on hypervelocity are predicted based on the modified model, which are in good agreement with the experiments.