Studies on the Optimum Mechanical Response of Anisotropic Materials Related to Elastic Constants

In this paper, mechanical and elastic behaviour of anisotropic materials are investigated in order to understand the optimum mechanical behaviour of them in selected directions. For an anisotropic material with known elastic constants, it is possible to choose the best set of elastic constants (effective elastic constants) which determine the optimum mechanical and elastic properties of it. For this reason, bounds on the anisotropic elastic constants have been constructed symbollicaly for all anisotropic elastic symmetries. As illustrative examples, materials from different symmetries are selected and their elastic constants are used to compute bounds on the anisotropic elastic constants. Finally, by examining numerical results of bounds given in tables, it is seen that the materials selected from the same symmetry type which have larger interval between the bounds, are more anisotropic, whereas some materials which have smaller interval between the bounds, are closer to isotropy. The construction of bounds on anisotropic elastic constants is a significant and critical case in design of any engineering and structural materials.