Molodtsov, I. N. Applied questions of Il’yushin theory of elastoplastic processes. (English. Russian original) Zbl 1487.74014 Mosc. Univ. Mech. Bull. 75, No. 5, 121-126 (2020); translation from Vestn. Mosk. Univ., Ser. I 75, No. 5, 33-38 (2020). Summary: The experimental results of the processes of complex loading along helical strain trajectories are used to find out that the response to the helical strain trajectory following the simple loading after exhaustion of some trace takes a certain shape of the limit mode, that is, there is a correspondence between the deformation trajectory geometry and the form of response. A new variant of constitutive equations for describing complex loading processes with strain trajectories of arbitrary geometry and dimension is considered. The vector constitutive equations and the system of differential equations for the four angles from the Frenet decomposition are obtained. It is proved that the stress vector is represented in the form of sum of three terms: rapidly decaying plastic traces of elastic states, instantaneous responses to the deformation process, and irreversible stresses accumulated along the deformation trajectory. A new method for mathematical modeling of five-dimensional processes of complex loading is constructed and tested on two- and three-dimensional processes. Cited in 2 Documents MSC: 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74A20 Theory of constitutive functions in solid mechanics Keywords:complex loading; vectorial constitutive equations; strain trajectory; stress trajectory; isomorphism theorem; functional calibration × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Il’yushin, A. A., Plasticity (1963), Moscow: Akad. Nauk SSSR, Moscow [2] A. S. Vavakin, R. A. Vasin, V. V. Viktorov, and R. I. Shirov, Experimental Study of Elastoplastic Deformation of Steel under Multiaxial Loading along Curvilinear Spatial Strain Trajectories, Available from VINITI, No. 7298-B86 (Moscow, 1986). [3] Zubchaninov, V. G., Isotropy postulate and the law of complex unloading of continua, Mech. Solids, 46, 21 (2011) · doi:10.3103/S0025654411010043 [4] Molodtsov, I. N.; Babaeva, D. O., Some mathematical models of elastoplastic processes of complex loading, Intell. Syst. Teor. Pril., 22, 19-36 (2018) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.