A case for Tsai’s Modulus, an invariant-based approach to stiffness

Abstract

For the past six years, we have been benefiting from the discovery by Tsai and Melo (2014) that the trace of the plane stress stiffness matrix (tr(Q)) of an orthotropic composite is a fundamental and powerful scaling property of laminated composite materials. Algebraically, tr(Q) turns out to be a measure of the summation of the moduli of the material. It is, therefore, a material property. Additionally, since tr(Q) is an invariant of the stiffness tensor Q, independently of the coordinate system, the number of layers, layup sequence and loading condition (in-plane or flexural) in a laminate, if the material system remains the same, tr(Q)=tr(A∗)=tr(D∗) is still the same. Therefore, tr(Q) is the total stiffness that one can work with making it one of the most powerful and fundamental concepts discovered in the theory of composites recently. By reducing the number of variables, this concept shall simplify the design, analysis and optimization of composite laminates, thus enabling lighter, stronger and better parts. The reduced number of variables shall result in reducing the number and type of tests required for characterization of composite laminates, thus reducing bureaucratic certification burden. These effects shall enable a new era in the progress of composites in the future. For the above-mentioned reasons, it is proposed here to call this fundamental property, tr(Q), as Tsai’s Modulus.