The ‘effective modulus’ in cubic single crystals subjected to full transverse constraint

Abstract

The orientation dependence of the ‘effective modulus’ relating the applied stress to the applied strain for a single crystal of a triclinic material subjected to full transverse constraint is specified as a general problem for which special solutions apply when conditions of symmetry exist. When the crystal is cubic and the direction of applied stress is along <100>, <110> or <111> directions, the ‘effective modulus’ is simply the elastic stiffness tensor c i j resolved along the direction under consideration. For all other orientations of cubic single crystals, this ‘effective modulus’ can be shown analytically to be less than the elastic stiffness tensor resolved along the direction under consideration.