Mathematical modeling of dynamic fracture processes in concrete

Abstract

We solve the problem on the collision of steel cylindrical hammers in the velocity range up to 800 m/s with rectilinear concrete slabs. We consider the following two approaches to calculating concrete fracture under impact loading: the phenomenological approach in which the strength criteria are expressed in terms of invariant constraints imposed on the critical macrocharacteristics of the process, i.e., stresses and strains, and the approach in which the fracture is considered as the process of formation, growth, and confluence of microdefects under the action of applied stresses. We compare the results of mathematical modeling with the experimental data concerning the penetration depth and the exterior flushing value. In the framework of the proposed model of dynamic fracture in concrete, we calculate the strength of a concrete tetrahedral prism under the action of longitudinal loads. We obtain a satisfactory agreement of the results of mathematical modeling with experimental results.