Behaviour Modelling of the Pseudo-Elastic-Plastic Material at Non-Stationary Loading

Abstract

The article is devoted to studying the behaviour of pseudo-elastic-plastic materials under significant deformations. The study of the behaviour of bodies from pseudo-elastic-plastic materials requires the development of special algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at a point is represented as the sum of the elastic component, the jump of deformation during a phase transition, plastic deformation and deformation caused by temperature changes. A numerical method of increased accuracy based on the use of two-dimensional spline functions for solving multidimensional non-stationary problems of the theory of thermo-elasticity for bodies made of pseudo-elastic plastic materials at large deformations is proposed. A phenomenological model is constructed to describe the properties of thermo-elasticity in a point with consideration of heat generated during phase transition in geometrically nonlinear formulation. Basic equations describing the behaviour of pseudo-elastic plastic materials at significant deformations and consisting of the equation of thermal conductivity, motion, physical and geometric relations are written. Numerical examples are considered.