Graphical Representation of the Generalized Hooke’s Law

Abstract

The anisotropic linear elastic behavior of single crystals can be described equivalently by a 4th-order elasticity tensor or two functions E(d) and K(d). These functions represent Young’s modulus and a generalized bulk modulus as functions of the tensile direction d in a tension test. In the present paper three- and two-dimensional graphical representations of Young’s modulus and the generalized bulk modulus are given for single crystals belonging to one of the following symmetry groups: monoclinic, rhombic, trigonal, tetragonal, hemagonal, and cubic symmetry.