A micromechanical constitutive model for concrete subjected to impact loadings

Concrete is considered as a four-phase composite consisting of an intact matrix and three mutually perpendicular groups of penny-shaped micro-cracks. The intact matrix is assumed to be elastic, homogeneous and isotropic. Based on Mori-Tanaka's concept of average stress in the matrix and Eshelby's equivalent inclusion theory, the compliance tensor of concrete is worked out, and the dynamic constitutive model for concrete is proposed. Meanwhile, micro-crack growth is also discussed. Experimental results show that both the concrete and cement mortar are rate-dependent. The peak stresses of the concrete and the cement mortar increase with the strain rate, and the fragment sizes of the concrete and the cement mortar decrease with the impact velocity. The theoretical prediction agrees well with the experimental data.