Bounds on the extensional strains in elastic homogeneous crystals under simple tension

Within the context of the linearized theory of elasticity, weconsider homogeneous crystals, which have orthorhombic, tetragonal,hexagonal symmetry or cubic symmetry (‘RTHC’ crystals).When such a crystal is subjected to a simple tension (or compression)of amount T in the direction n, there will be three, generallydifferent, extensional strains along the three mutually perpendiculardirections corresponding to the principal axes of strain. Thepurpose of this paper is to present a simple procedure to placebounds, upper and lower, on the possible extensional strainsin the crystal, both in the case when n is fixed in directionand in the case when n is arbitrary. The procedure allows usto determine whether the bounds are attained or not.