Tangent Moduli of the Hencky Material Model Derived from the Stored Energy Function at Finite Strains

Abstract

Tangent moduli associated with the linear logarithmic model of hyperelasticity are derived. These relations are crucial not only to theoretical analyses but also to wave propagation and ultrasonic testing. The tangent moduli as functions of stress determine the speed of propagating acoustic waves and, therefore, indirectly point to a possible occurrence of residual stress fields in elastic solids.