Universal deformations of a compressible transversely isotropic body
A deformation is called universal if the displacements satisfy equilibrium equations of hyperelasticity (that is of existence of an elastic potential). \textit{J.-L. Ericksen} [J. Math. Phys. 34, 126-128 (1955; Zbl 0064.421)] proved that a compressed transversally isotropic medium has a universal solution if and only if a transformation of initial shape (of a bounded body) into the final shape is affine. The author offers a short proof of this property for a transversally isotropic anisotropic body.
transversally isotropic anisotropic body
scientific article; zbMATH DE number 4039396