Further developments of physically based invariants for nonlinear elastic orthotropic solids

Recently, Rubin and Jabareen (J. Elast. 90:1-18, 2008) introduced six physically based invariants for nonlinear elastic orthotropic solids which are measures of distortions that cause deviatoric Cauchy stress. Three of these invariants include three dependent functions that characterize the distortion in a hydrostatic state of stress. In particular, these invariants can be used without the need to place additional restrictions on the strain energy function to model the distortion in a hydrostatic state of stress. The objective of this research note is to modify the definitions of the remaining three invariants. These new invariants have clear physical interpretations that can be measured in experiments.