The Behaviour in the Rubber‐Like State: Finite Strain Elasticity

The generalised deformation of strain has major importance for deformation of rubbers where the strains are generally not small. The role of rigid body rotations, polar decomposition and principal extension ratios are explained, together with examples of elementary strain fields, logarithmic strain and the stress tensor. Stress-strain relationships are developed for finite strain analogous to the generalised Hooke's Law for small strains. The use of a strain function for finite deformation requires thermodynamic considerations i.e. the relationship to Helmholtz and Gibbs free energies. Finally, consideration of the formulation of the strain energy in terms of strain invariants or, more directly, extension ratios.