Abstract For the past six years, we have been benefiting from the discovery by [1] 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.

中文翻译：

---

蔡氏模量的一个案例，一种基于不变量的刚度方法

摘要 在过去的六年中，我们一直受益于 [1] 的发现，即正交各向异性复合材料的平面应力刚度矩阵 ( tr ( Q ) ) 的迹线是层压复合材料的基本且强大的缩放特性。在代数上， tr ( Q ) 是材料模量总和的度量。因此，它是一种物质属性。此外，由于 tr ( Q ) 是刚度张量 Q 的不变量，如果材料系统保持不变，则与坐标系、层数、铺层顺序和层压板中的加载条件（面内或弯曲）无关, tr ( Q ) = tr ( A * ) = tr ( D * ) 还是一样的。所以，tr ( Q ) 是人们可以使用的总刚度，使其成为最近在复合材料理论中发现的最强大和最基本的概念之一。通过减少变量数量，这一概念将简化复合层压板的设计、分析和优化，从而实现更轻、更坚固和更好的部件。变量数量的减少将导致复合层压板表征所需测试的数量和类型减少，从而减少官僚认证负担。这些影响将使未来复合材料的进步进入一个新时代。由于上述原因，这里建议将这个基本性质 tr ( Q ) 称为蔡氏模数。分析和优化复合层压板，从而实现更轻、更强和更好的部件。变量数量的减少将导致复合层压板表征所需测试的数量和类型减少，从而减少官僚认证负担。这些影响将使未来复合材料的进步进入一个新时代。由于上述原因，这里建议将这个基本性质 tr ( Q ) 称为蔡氏模数。分析和优化复合层压板，从而实现更轻、更强和更好的部件。变量数量的减少将导致复合层压板表征所需测试的数量和类型减少，从而减少官僚认证负担。这些影响将使未来复合材料的进步进入一个新时代。由于上述原因，这里建议将这个基本性质 tr ( Q ) 称为蔡氏模数。