New universal relations for nonlinear isotropic elastic materials

New universal relations for nonlinear isotropic elastic materials

A nonlinear isotropic elastic block is subjected to a homogeneous deformation consisting of simple shear superposed on triaxial extension. Two new relations are established for this deformation which are valid for all nonlinear elastic isotropic materials, and hence are universal relations. The first is a relation between the stretch ratios in the plane of shear and the amount of shear when the...

Additional Universal Relations for Transversely Isotropic Elastic Materials

For the case of distinct eigenvalues of the left Cauchy-Green tensor universal relations for a transversely isotropic elastic material are expressed in a compact form. Also, two new universal relations are derived for an incompressible transversely isotropic elastic material. Key Wolds: universal manifold, incompressible materials, simple shear, annular wedge 1. INTRODUcnON A universal relation...

Nonlinear elastic inclusions in isotropic solids.

We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construc...

Relations between loss angles in isotropic linear viscoelastic materials

For the description of the mechanical behaviour of linear viscoelastic materials a number of characteristic material properties is in use. So the relaxation functions in shear, J(t), in extension, D(t), and in compression, B(t), describe the response of the material to a stepfunction H(t) in the corresponding stress. It can be shown theoretically that the relaxation functions are monotonically ...

Universal Solutions and Universal Relations for Some Types of Elastic Fluid Crystals*