quasi-static process, the theorem on implicit functions, stress, strain, elasticity, area attraction.

Discusses the problem of the existence of a quasi-static process, described by the solution of a system of differential equations in matrix form. Formulated and proved a theorem that allows to study this problem. It is shown that if the external effects are potential, the study can be conducted on the basis of the theorem of implicit functions in the framework of statics. 

1. Minaeva, Nadezhda Vitalevna Dr. Sci. Phys. & Math., Professor, Voronezh State University of Engineering Technologies, Voronezh

2. Shashkin, Aleksander Ivanovich Dr. Sci. Phys. & Math., Professor, Dean of the faculty of applied mathematics and mechanics, Voronezh State University, Voronezh