A non-Gaussian network model for rubber elasticity

A simple constitutive model based on the non-Gaussian, Kuhn-Grün probability distribution function is derived. It is assumed that the actual macromolecular structure of a rubber-like material can be replaced by idealized equilateral tetrahedra cells that are not mutually exclusive so far as occupancy of the space is concerned. The three chains are assumed to meet at a junction point located at the centroid of the cell with their other ends being fixed at the vertices of the equilateral tetrahedron. The centroid junction point is free to fluctuate, subject to the constraint imposed by the equilibrium of chain forces. Stress-stretch constitutive equations are then derived to study homogeneous deformations of isotropic, incompressible hyperelastic rubber like materials. The accuracy of the derived constitutive equations is demonstrated by using uniaxial, equibiaxial, pure shear, and plane strain experimental data provided in the literature.