Nonlinear Mechanics of Continuous Media

The training manual is devoted to a systematic setting of the fundamentals of the mechanics of a continuous medium with finite deformations. The kinematics of continuous media, universal laws of conservation of the mechanics of a solid medium, the theory of jumps of functions on the surfaces of strong gaps are considered. The theory of progenic derivatives, dynamic solids of deformations, principles of material indifference and material symmetry is provided in a systematic form. A new approach to the formulation of determining relations for elastic and inelastic media with finite deformations, based on the use of energy and quasi-energy pairs of strain stress tensors, is proposed. With this approach, the theory of finite elastic and viscoelastic deformations, the theory of large plastic deformations, anisotropic media with large deformations is presented.
The textbook contains a significant number of exercises.
A training manual is intended to be student and graduate students studying in physical and mathematical and engineering specialties, as well as specialists engaged in various issues of solid medium mechanics