Efficient dynamic equation for compositional mean isotropic elastic body

The article presents effective dynamic equations for mean isotropic solid in stresses and displacements. We have established that the structure of equations in both cases is completely preserved as in the homogeneous case within the accuracy of replacement of deformations, stresses and displacements by average values in representative volume of the composite solid. At the same time, it is necessary to use the previously obtained average Kravchuk - Tarasyuk values of Young's modulus, Poisson's ratio, shear modulus as average elastic characteristics. The equations are obtained in the existence of a connection between the effective values of the elasticity modulus, Poisson's ratio, the shear modulus of a similar well-known coupling for the coefficients of a body from one homogeneous material. Since this connection is approximate even in the homogeneous case, this has little effect on the accuracy of the equations obtained. Effective values of the propagation velocities of various types waves in a composite in average isotropic medium are obtained. The results of these studies allow solving dynamic problems for solid composite bodies using standard finite element support, for example ANSYS. The data obtained in our research allow us to recommend using not only the average for Kravchuk - Tarasyuk elastic parameters, but also the average density of the composite solid, also calculated in Kravchuk - Tarasyuk approximation as the effective characteristics of solids.