Hybrid functions of the second kind in the mechanics of a deformable solid

A mathematical definition of the concept of a «hybrid function of the second kind» (GF2) is given, which differs from a «hybrid function of the first kind» (GF1) in that GF2 completely lacks the connection of arguments of basic functions with arguments of control complexes. Therefore, the number of parameters in GF2 has been increased from three to four. But at the same time, it becomes possible to control GF2 both by a continuous argument and by a discrete one. The possibility of constructing chain functions (CGF2) remains, and any combinations of GF1 and GF2 are possible. The hybrid GF2 function is a function for describing processes that are spaced both in time and space, for example, for studying layered media with different physical and mechanical properties. The article provides an example of a study of the elastic-plastic stress state in a three-layer beam, the layers of which consist of materials with different deformation diagrams. Another example relates to the mathematical modeling of the crack growth process in a flat sample. In this case, the crack growth processes with the corresponding velocities are separated in time. A hybrid function is proposed for modeling the behavior of a complex technical system with negative feedback, which allows to automatically extinguish disturbances arising during the operation of the system.

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