Studies on the Optimum Mechanical Response of Anısotropıc Materials Related to Elastıc Constants

Abstract

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.