Simulation of the behavior of a rod from three-linear two-phase material taking into account temperature

In the conditions of modern scientific and technological progress in various fields of science and technology an increasing number of new materials find application. The growth of production of pseudo-elastic-plastic materials or materials with shape memory which have phase transitions and their wide application necessitate the creation of new mathematical and computer models and calculation methods taking into account real technological loads and material properties. To simulate the behavior of structural elements made of such materials it is necessary to determine the unsteady thermomechanical state not only at the pseudo-elastic stage of deformation, but also beyond the elastic limit at significant plastic deformations. In order to construct physical relations between the stress and strain, it is necessary to know the position of the phase transition front and the kinetic response function. Such a problem is relevant for mathematical and computer simulation of materials having phase transitions with regard to temperature. The paper formulates a nonlinear phenomenological model for describing the properties of alloys with memory at the material point and during temperature changes. It has been established that classical material diagrams are a curve enveloping a certain family of material diagrams constructed according to certain laws of changes in the rate and discontinuity of the deformation front. In order to use the phenomenological model to investigate two-phase materials with different elastic moduli, an additional problem related to the development of the instantaneous thermomechanical surface is introduced. A numerical study has been carried out in the work, as a result of which a typical dependence for the phase transition propagation velocity in time has been obtained. The graph of the dependence of the phase transition propagation velocity on time has three sections. On the first section the speed is zero, and on the third it reaches a constant value. Between them there is a section with a variable velocity. As a result of calculating the tangential modulus at each time integration step, the integral material diagram constructed in the work also has three characteristic sections. The phenomenological model obtained in the paper can be used for mathematical and computer modeling of functional materials