PRACTICAL NON-LINEAR ELASTICITY THEORY FOR LARGE STRAINS

Abstract

We present a theory of non-linear elasticity, of finite deformation, in which real stress-strain relationships are set up and defined thermodynamically. Relationships between these quantities and the standard third-order elastic stiffness coefficients c _IJK are given. The utility of these quantities is demonstrated by easy derivations of the pressure coefficients of the second-order elastic constants c _IJK , and of the acoustic velocities in materials under elastic strain.

Keywords:

• Finite deformation
• Elasticity
• Non-linear