Modeling of rectification of a nonlinear-elastic cylindrical layer taking into account the change in the direction of transversal isotropy

The article considers a mathematical model of the deformation of a body made of an incompressible transversally isotropic nonlinear elastic material. Particular attention is paid to the vector characteristic of a transversally isotropic body, which indicates the direction of the axis of transversal isotropy, as well as to the change in this characteristic during deformation. It is noted that under deformation of a certain type, a transversely isotropic material behaves like a Treloar material. A special case of the problem of deformation of an incompressible transversally isotropic nonlinear elastic cylindrical layer is studied, and an exact analytical solution of the problem is obtained for this case.