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

Albertino Arteiro, Naresh Sharma*, Jose Daniel D. Melo, Sung Kyu Ha, Antonio Miravete, Yasushi Miyano, Thierry Massard, Pranav D. Shah, Surajit Roy, Robert Rainsberger, Klemens Rother, Carlos Cimini, Jocelyn M. Seng, Francisco K. Arakaki, Tong Earn Tay, Woo Il Lee, Sangwook Sihn, George S. Springer, Ajit Roy, Aniello RiccioFrancesco Di Caprio, Sachin Shrivastava, Alan T. Nettles, Giuseppe Catalanotti, Pedro P. Camanho, Waruna Seneviratne, António T. Marques, Henry T. Yang, H. Thomas Hahn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Article number112683
JournalComposite Structures
Early online date09 Jul 2020
Publication statusPublished - 15 Nov 2020


  • Analysis
  • CFRP
  • Invariants
  • Stiffness

ASJC Scopus subject areas

  • Ceramics and Composites
  • Civil and Structural Engineering


Dive into the research topics of 'A case for Tsai's Modulus, an invariant-based approach to stiffness'. Together they form a unique fingerprint.

Cite this