Hybrid Functions of the Second Kind in the Mechanics of Deformable Solid Bodies

A mathematical definition of the concept of “second-kind hybrid function” (HF2) is given. This function differs from the “first-kind hybrid function” (HF1) in that HF2 has no relationship between the arguments of the base functions and arguments of the control complexes. As a result, the number of parameters in HF2 increases from three to four. However, this allows for control of HF2 by both continuous and discrete arguments. The possibility of constructing chain functions (CHF2) is preserved, and any combinations of HF1 and HF2 are possible. The hybrid function HF2 can describe processes that are separated both in time and space. It is used, e.g., to study layered media with different physical and mechanical properties. An example is provided regarding the investigation of the elastoplastic stressed state in a three-layer beam, where the layers consist of materials with different deformation diagrams. Another example pertains to the mathematical simulation of the crack growth process in a flat sample. In this case, the crack growth processes with corresponding speeds are separated in time. A hybrid function is proposed for simulation of the behavior of a complex technical system with negative feedback, which allows for the automatic damping of disturbances occurring during the operation of the system.