Modelling and simulation of the localized plastic deformation by relaxation element method

In the present work a new and a little known method of modelling and simulation of plastic strain localization in a loaded solid - relaxation element method (REM) is presented. The fundamental property of solid: “Plastic deformation of solid under loading is accompanied by stress relaxation in the local volume of it” lies in the basis of the method. The theoretical grounding of the method from the point of view of constitutive equations of theory of elasticity and continuum theory of defects is conducted. For the plane-stress state the technique of construction of local sites of plastic deformation by the method on the mesoscopic scale level is demonstrated. The technique of calculation of stress state of the plane with the sites of different shape and gradients of plastic deformation is described. The new type of relaxation elements, different from ones used in the works [1-6] has been applied. This allowed to extend the method on the new class of objects. The examples and the results of simulation of the processes of plastic strain localization, accompanied by the effect of Luder’s band propagation and Portevin Le Chatelier Effect are considered. The examples show, that REM is a comfortable tool when simulating the effect of plastic strain localization on meso- and macro- level.