Three-Dimensional Systems

Medium elastic properties are based on the stress - strain relations

Stress T ... force dF per unit area dA

acting on the surface of a differential volume element of a solid body:

Strain S  ...  change in length per unit length

Both T and S are second rank tensors

Stress-strain relation can be written in a form of the generalized Hooke's law as:

where [c] ... stiffness matrix

          [s]  ... compliance matrix

Stiffness coefficients of silicon are:

• Bulk waves
  • Longitudinal waves

  phase velocity:  

  • Transversal waves

 phase velocity:  

• Surface waves

Approximation of the Rayleigh wave velocity in a homogeneous substrate: