Elements of the Nonlinear Theory of Elasticity Based on Tensor-Nonlinear Equations

The chapter contains information that forms the basis of a new direction in the nonlinear theory of elasticity. The theory, having adopted the mathematical apparatus obtained in the middle of the last century, after its analysis, is used with significant changes. This concept allows us to more accurately reveal the mechanism of deformation of materials, the elastic nature of which significantly depends on the type of stress state, due to the growth of additional volumetric deformation associated with the accumulation of defects, called dilatation. The work is original — after abandoning the elasticity characteristics in the form of modules - constants, the main role is assigned to material functions, which represent statistical characteristics. Their relation can be considered a coefficient of variation and a parameter of tensor nonlinearity, which makes it possible to represent the deformation in the form of two parts, different in origin.