A new theory of the stored energy in elasto-plasticity and the torsion test

According to the classical elasto-plastic theories the stored energy ratio is an increasing function of the axial deformation in a traction test. Measurements using a microcalorimeter or an infra-red camera have evidenced a decrease of the same ratio. There exists an agreement between these experimental results and a new, one dimensional elasto-plastic theory elaborated by A. Chrysochoos, O. Maisonneuve and their collaborators in the period 1985-1987. We give a three dimensional generalization of the new theory. In this way various complex loading processes can be analysed taking into account the new elasto-plastic model. We show that according to the new theory the stored energy ratio is a decreasing function of time during a torsion test, in which the elasto-plastic state of the body is non-homogeneous. Also, in the frame-work of the new theory, we determine the time evolution of the temperature on the lateral surface of a torsioned circular bar. In this way an experimental verification of the new theory becomes possible, by determining the evolution of the surface temperature during a torsion test using infra-red thermography.