Mathematical model of static-dynamic deformation of concrete

Abstract

This article examines the obtaining of the design parameters of the diagram of the static - dynamic deformation of concrete under various loading conditions. The basic differential equation of the variant of the deformation model of complexly stressed concrete of the relationship "strain intensity - stress intensity" for the mode of its static-dynamic loading and its solution at various levels of initial static stress, which allows to determine the parameters of the diagram of static- dynamic concrete deformation, in particular, the ultimate deformability of concrete and dynamic limit of its strength at regime static-dynamic loading. The limiting deformability of concrete is calculated at various levels of its initial static loading under the simplest stress state - uniaxial compression. A basic differential equation and a variant of deformation dependences are constructed to determine the parameters of the diagrams of the static-dynamic deformation of concrete under uniaxial compression "strain intensity - stress intensity" for a two-stage mode of its static-dynamic loading and a solution to this equation is obtained at various levels of init ial static stress and dynamic (shock) loading.