On a Relationship Between Normal-Shear Coefficients and Tensile Moduli in Anisotropic Materials

In general, stress and deformation tensors of anisotropic linear elastic materials are related by the fourth order compliance/elasticity tensor. It has been observed that in the case of a planar (2D) orthotropic material the off-diagonal component of the compliance tensor known as normal-shear coefficient is equal to one half of the derivative of corresponding tensile compliance with respect to the angle of rotation of coordinate axes. A detailed analysis of the transformation law for the components of the compliance tensor is given, including the proof that the same relation also holds in the general case of planar anisotropic materials. In the selected illustrative examples polar diagrams of tensile moduli and normal-shear coefficients are shown for representative cases of woven fabrics and textile composites