Peculiarities of Behavior of Simplest Models of Nonlinear Elasticity Constructed Based on New Holonomic Tensor Measures

Abstract

We consider new holonomic tensor measures of strain and stresses and build nonlinear elasticity models for which the problems of stretching of a thin wide plate and uniaxial stretching of a rod from incompressible materials are solved. These models are congruent with classical ones when deformation is small, and they essentially demonstrate various properties at large deformations.