Analysis of reinforced-concrete strength under impact loading

Abstract

A mathematical model is proposed to describe deformation and fracture of reinforced concrete under impact loading within the framework of mechanics of continuous media. The problem of the impact of steel cylindrical projectiles on rectangular slabs made of reinforced concrete is solved. The results of mathematical modeling are in good agreement with experimental data.The problem of impact interaction of cylindrical projectiles with rectangular concrete and reinforced-concrete slabs was solved in [1][2][3]. Concrete fracture was calculated by a phenomenological approach where the strength criteria are expressed in terms of invariant relations between the critical values of macrocharacteristics of the process (stresses and strains). Until the failure criterion is reached, the concrete behavior under dynamic loading is described by the model of a linear elastic body possessing physical and mechanical properties of concrete. As the failure criterion is satisfied, the material is assumed to be damaged by cracks. Fragmentation of the damaged material is described within the framework of the model of a porous elastoplastic medium. Fragmentation of the crack-damaged material subjected to tensile stresses occurs when the relative volume of voids reaches a critical value. If the crack-damaged material is subjected to compressive stresses, the local criterion of fragmentation is either the limiting value of the work of plastic strains or the limiting value of intensity of plastic strains, which is uniquely related to the first factor. The fractured material behaves as a granulated medium that can withstand compressive and shear stresses but fails under the action of tensile stresses. The results of mathematical modeling of impact interaction of steel cylindrical elements with concrete slabs compared with experimental data showed that this approach can be used to calculate the strength of elements of reinforced-concrete structures under dynamic loading.In calculating reinforced-concrete structures, the concrete layer with reinforcing bars is modeled by an elastoplastic medium, which is a homogeneous two-phase mixture of steel and concrete. In contrast to concrete whose typical feature is brittle fracture, the fracture of the homogeneous two-phase mixture of steel and concrete is rather similar to that of plastic materials [4].A mathematical model that allows calculating deformation and fracture of high-strength porous ceramics under explosive and impact loading within the framework of mechanics of continuous media was developed in [5][6][7]. An advantage of this model is the possibility of studying the fracture in porous ceramics under multiple impact loading. This mathematical model was used in [8] to study the mechanisms of particle refinement for obtaining submicron powders in a pneumatic circular machine. This model can be readily adapted to calculating the strength of foam concrete under dynamic loading.