Incremental elastic coefficients of an isotropic medium in finite strain

Summary

Incremental elastic coefficients are derived for an isotropic medium in a state of finite initial strain. The analysis is based on concepts and methods developed by the author in earlier publications¹)²)³)⁵) which require only elementary procedures and bring to light the physical significance of the results. Remarkably simple formulas for the incremental shear coefficients are established. For comparison the same results are derived by an alternate procedure using Riemannian tensors and the calculation is shown to be much more elaborate. Application is made to the particular case of second order elasticity theory and expressions derived for the incremental coefficients including the correction terms of the first order in the initial strain. This provides a complete theory of first order correction for acoustic propagation under initial stress.