Dynamic spherical cavity expansion analysis of concrete using the Bingham liquid constitutive model

High pressure exists in concrete targets during hypervelocity penetration. An incompressible concrete material under large deformation can be represented by a liquid constitutive model. The present work modifies the cavity expansion theory by characterizing incompressibility using the Bingham liquid constitutive model, in which the viscosity of an incompressible material is considered according to Cleja-Tigoiu's work. An analytic expression is derived for the relationship between the pressure on a cavity boundary and the velocity of cavity expansion. 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. The viscosity coefficient (μ₀) is the most sensitive parameter for the radial stress on the cavity surface. As μ₀ increases, the dimensionless stress on the cavity surface (S) increases and the quadratic relation between S and the velocity of cavity expansion (a˙) becomes weaker. Finally, the penetration depths of long rod hypervelocity penetration into a concrete target are predicted based on the modified model, the results are in good agreement with experimental results.