A note on the dynamic spherical cavity expansion of concrete with shear dilatancy

Considering the compression and dilatation of the concrete, a model of dynamic spherical cavity expansion is constructed, where the complete response of target is densification region-dilatation region-crack region-elastic region, and the dilatant-kinematic relation is used for the dilatation region. The expression of cavity stress and expansion speed is obtained with the theory above, and the depths of penetration in different conditions are calculated. The effects of the concrete strength and dilatation on penetration depth are analyzed. The results indicate that the proposed model is reasonable to predict the depth of penetration; the stress hardening parameter has a great influence on the depth of penetration, and the shear saturation should be considered with the increase in the projectile volecity; with the decrease in the densification parameter, the condition of the concrete turns into dilatation from compression, resulting in the increase in cavity stress and the decrease in depth of penetration.