Conditions of elastic mechanical stability and elastic properties of crystal structures with different symmetry
А. I. Gusev, С. И. Садовников
Abstract
A critical analysis of the conditions of elastic stability of crystal structures of different symmetry as restrictions imposed on their elastic constants c ij has been carried out. It is shown that the conditions of elastic stability of all crystals, except for cubic ones, are described by polynomials from the second to sixth powers of their elastic constants c ij . Necessary and sufficient conditions for the elastic stability of crystals of different symmetry are presented explicitly. Keywords: Elastic stability, Symmetry, Elastic constants, Stability conditions.
Topics & Concepts
Symmetry (geometry)Stability (learning theory)Materials scienceElasticity (physics)Constant (computer programming)Condensed matter physicsStructural stabilityPhysicsMathematical analysisClassical mechanicsMathematicsThermodynamicsGeometryStructural engineeringComputer scienceMachine learningEngineeringProgramming languageMaterial Properties and ApplicationsMaterial Science and ThermodynamicsMaterial Properties and Failure Mechanisms