Calculation of changes in state of Murnaghans elastic-plastic material under conditions of flow with known movement speeds

Abstract

For the generalized elastic-plastic material of Murnaghan, the problem of determining the velocities of the left measure of elastic distortions and the growth parameter of elastic deformation anisotropy at known displacement velocities is considered. The defining equations are formulated in a finite form for the specific potential energy of elastic deformation and the Cauchy stress tensor. Differential defining equations are presented for the stresses potential, stresses and anisotropy parameters. Three possible cases when the point of the deviator section of the yield surface will be regular or singular are considered. A system of equations for determining the velocities of the right-hand measure of elastic distortions and the growth parameter for elastic anisotropy is obtained. Using an orthogonal transformation with proper orthogonal rotation tensor that accompanies an elastic deformation, the system is reduced to a system of equations for determining unknown parameters. With the help of the symbolic calculation tools of the MathCAD 8 system, the necessary analytical representations of the values for the developed program complex in the FORTRAN language are found. The procedure for minimizing the growth parameter of elastic deformation anisotropy is described. A software implementation of the solution of this problem is obtained, which is an essential element of the numerical simulation system for the material under consideration.