Estimation of 3D Effects in Deformation of the Window Material Plates in Exploding Foils Experiments

In this work the theoretical background of an experimental technique for measuring of the Poisson adiabatics of window materials in the pressure range of 0.5 - 8 GPa is presented. It has been shown that for the development of such technique it is necessary to evaluate reasonably the three-dimensional effects of deformation of the window material plates in the dynamic experiments [1,2]. To carry out such an assessment, the equations of elasticity theory and the boundary conditions for the problem of compression of an elastic body, having the shape of a rectangular parallelepiped, one of the faces of which is pressed by a piston and all other faces are free, were written down. The equations describing the deformation dynamics were solved by the method of successive approximations, considering the Poisson coefficient as a small parameter. In this work, a solution of the equations in the zeroth approximation has been found, and a system of the equations and boundary conditions for the displacement vector in the first approximation has been derived. The solution of this system of equations will allow us to study the nature of the three-dimensional deformation of the window material plates.