Elements of elasticity theory

In this chapter, a review of the basic principles of elasticity is carried out. We define the concepts of wave, elasticity, isotropy, strain, stress (both normal and shear) and the most usual elastic moduli (Young’s modulus, Poisson’s ratio, bulk modulus, etc.). A relationship between the bulk modulus, the Poisson ratio and the Young modulus is deduced. Without derivation, equations which link the compressional and shear velocities with the elastic moduli are given. This chapter carries out a review of the basic principles of elasticity. It defines the concepts of wave, elasticity, isotropy, strain, stress (both normal and shear) and the most usual elastic moduli (Young’s modulus, Poisson’s ratio, bulk modulus, etc.). A relationship between the bulk modulus, the Poisson ratio and the Young modulus is deduced. Without derivation, equations which link the compressional and shear velocities with the elastic moduli are given. In the derivations, it is assumed that the rocks are homogenous, isotropic and elastic. The chapter shows the typical behaviour of an elastic material when stressed. Beyond a certain strain known as the “limit of elasticity”, the strain-stress relationship is no longer linear. Rocks tend to behave as elastic solids when disturbed by seismic waves. However, beyond a certain strain known as the “limit of elasticity”, the strain-stress relationship is no longer linear. If the stress continues to increase, eventually the fracture point is reached, where the sample breaks down.