On the Extreme Values of Young’s Modulus, the Shear Modulus, and Poisson’s Ratio for Cubic Materials
M. Hayes, Alexander Shuvalov · Journal of Applied Mechanics · 1998
For homogeneous cubic elastic materials with positive definite stored energy it is shown that the maximum and minimum values of Young’s modulus E are related to the maximum and minimum values of the shear modulus G through the simple connection 1/Gmin−1/Gmax=3(1/Emin−1/Emax). It is deduced that the ratio of compliances −s12/s44 is the maximum value of Poisson’s ratio v in the cubic materials with a positive parameter χ=2s11−2s12−s44, and the minimum value of ν in the cubic materials with negative χ.