Necessary and Sufficient Elastic Stability Conditions for Single Crystals

Abstract Necessary and sufficient elastic stability conditions for single crystals for the seven crystal systems are specified for both stiffness and compliance tensors. For Laue classes of four of these crystal systems, conditions for the positive-definite forms of suitably chosen 4 × 4 real symmetric matrices are shown to be both useful and relevant. Other supposedly equivalent and often simpler conditions proposed in the literature for tetragonal, orthorhombic and monoclinic crystal systems are analysed; all are shown to be incorrect.