The work is devoted to the analysis and development of one of the fundamental directions of well-known prominent scientists in the field of linear and nonlinear hereditary chronomechanics of a solid deformable body, using generalized time. In connection with the 90th anniversary of the birth of senior researcher I.I. Bugakov and the 105th anniversary of the professor, head of the theory of elasticity of Leningrad State University L.M. Kachanov and Academician of the USSR of the Academy of Sciences, Head of the Department of Plasticity Theory of Moscow State University Yu.N. Rabotnov. Since 1969, the author studied under Ilya Izrailevich and Lazar Markovich, performed various scientific topics under their supervision, and studied the works of Rabotnov. Bugakov paid great attention to the principles of hereditary mechanics of deforming rheological complex media, building endochronic models of elastic-viscous plasticity with “simple” and “complex”, mainly horizontal, time scaling, using different physical, chemical and mechanical analogies for stable and aging media, which is reflected in 3 monographs, articles, PhD and doctoral dissertations [1]. Kachanov and Rabotnov dealt with the problems of mechanics of plasticity, creep, and fracture [2, 3], using time-temperature transformation. Almost at the same time (in 1997 and 1998) they developed and published close to each other theories of damage accumulation. In contrast to the approaches of Bugakov, in our works on elastoplasticity, we obtained quasilinear hereditary integral relations in the transformed time scale of a horizontal functional form (with a prehistory) by a nonlinear scale of a hierarchical structure, which makes it possible to describe the behavior of media with hardening and softening (with accelerated and slowed down response), modeling nonmonotonic deformation processes. The endochronic meaning of the theory of nonlinear elasticity and creep of Rabotnov with the introduction of a “simple” vertical scale of tension is established. Endochronic criteria for damage accumulation and durability by scaling time are proposed. The universal viscoelastoplasticity equations, constructed experimentally for various materials, were constructed using 2-d scaling [4], allowing to describe all phases of deformation and destruction.
This work was executed at partial support by a grant from St. Petersburg State University. (Activity 3, id 26130576).