1.3 Elastic properties

Abstract

In this chapter, the strain and stress tensors are defined and their main properties are derived. The elastic tensors, elastic stiffnesses and elastic compliances are then introduced. Their variation with orientation, depending on the crystal class, is given in the case of Young's modulus. The next part is devoted to the propagation of waves in continuous media (linear dynamic elasticity and the Christoffel matrix); the relation between the velocity and the elastic constants is given for the cubic, hexagonal and tetragonal classes. The experimental determination of elastic constants and their pressure and temperature dependence are discussed in separate sections. The last two sections of the chapter concerns nonlinear elasticity (second and higher-order elastic constants) and nonlinear dynamical elasticity. Keywords: Eulerian description; Hooke's law; Lagrangian description; Poisson's ratio; Voigt notation; Young's modulus; bulk modulus; compressibility; cubic dilatation; dynamic elasticity; elastic compliances; elastic constants; elastic stiffnesses; elastic strain energy; elastic waves; elasticity; elongations; energy density; harmonic generation; homogeneous deformation; polarization; pulse-echo technique; pulse-superposition method; resonance technique; shear; spontaneous strain; strain field; strain tensor; stress tensor