J Elast (2011) 103: 289–294 DOI 10.1007/s10659-010-9276-3 RESEARCH NOTE Further Developments of Physically Based Invariants for Nonlinear Elastic Orthotropic Solids M.B. Rubin · M. Jabareen Received: 8 June 2010 / Published online: 12 October 2010 © Springer Science+Business Media B.V. 2010 Abstract 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 func- tions that characterize the distortion in a hydrostatic state of stress. In particular, these in- variants 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. Keywords Elasticity · Invariants · Nonlinear · Orthotropic Mathematics Subject Classification (2000) 74B20 · 15A72 · 34B15 1 Introduction Criscione and his coworkers [2–4] have been developing invariants for nonlinear elastic isotropic and transversely isotropic solids which are physically based and yield nearly or- thogonal response. Recently, Rubin and Jabareen [7] introduced physically based invariants for nonlinear elastic orthotropic materials. In that formulation use was made of the work of Flory [6] to separate the kinematics of dilatation and distortion and the strain energy function was taken to depend on seven invariants: the dilatation J and six measures of distortion β i (i = 1, 2,..., 6). The invariants β i are measures of distortion which cause deviatoric stress. Specifically, {β 1 ,β 2 ,β 3 } depend on three dependent functions η i (J ) (i = 1, 2, 3) which M.B. Rubin ( ) Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, 32000 Haifa, Israel e-mail: mbrubin@tx.technion.ac.il M. Jabareen Faculty of Civil and Environmental Engineering, Technion—Israel Institute of Technology, 32000 Haifa, Israel e-mail: cvjmah@techunix.technion.ac.il