The determining the ratio of the mechanics of the continuous environment. Development of a mathematical apparatus

The book is devoted to the development of mathematical foundations and apparatus of the general theory of the determining relations of classical mechanics of continuous media with arbitrary deformations. It summarizes the achievements of modern domestic and foreign studies and proposed original results on the tensor representation of mechanical characteristics, clarifying the general mathematical structure of their connections in determining relations, on the development of axiomatics and the basics of theory. The mathematical apparatus of objective tensors and the systems connecting them from the system of reflection and equations has been developed, and the generalization of objective derivatives was introduced. New classes of tensor voltage measures and final deformations were built, including known measures. A variant of the theory of determining relations is proposed, agreed with the approaches of Ilyushin and Noll, axiomatically taking into account the possible presence of internal kinematic connections and fields of internal mass forces in the body. The generalization of the concepts of the image of the process and the properties of five -dimensional isotropy on the area of ​​final deformations is given.
For scientists and engineers, students and graduate students of universities and technical universities in the specialty "mechanics", teachers