Some mathematical models of elastoplastic processes of complex loading

In the framework of the Ilyushin’s theory of elastoplastic processes, in [3] for mathematical modeling of complex loading processes we use special type quasilinear equation with three state functionals. The functionals was calibrated using the experimental results [4] (R.A.Vasin, etc.) for 3D- helical trajectories of deformations. It turned out that the response on a helical trajectory of deformation takes a completely definite loading form, not exactly, but after the exhaustion of some trace of retard. On the helical trajectories of deformations the form of loading is the same: helical trajectory of deformations is becoming to helical trajectory of loading there and back. The used map preserves the geometry of space. This correspondence by Ilyushin is called as isomorphism theorem. All new theories use as the basis the directing vector of stresses and vectors constructed on the base of Frenet basis. For high-dimensional processes, the number of state functionals increases, so and the methods of their identification become more complicated. All models are completly verified. The results are given below.