On the extreme values of young's modulus, the shear modulus, and Poisson's ratio for cubic materials

摘要

For homogeneous cubic elastic materials with positive definite stored energy it is shown that themaximum and minimum values of Young's modulus E are related to the maximum and minimumvalues of the shear modulus G through the simple connection 1/G{sub}min - 1/G{sub}max = 3(1/E{sub}min - 1/E{sub}max). It is deduced that the ratio of compliances - S{sub}12/S44 is themaximum value of Poisson's ratio v in the cubic materials with a positive parameter X≡2S{sub}11- 2S{sub}12 - S{sub}44, and the minimum value of v in the cubic materials with negative X.