2.2 Mechanical field in a solid

In the case of linear elasticity and isotropic materials, the dynamic behavior of mechanical systems can be described by the following partial differential equation

 

$${\frac{E}{2(1+\nu)}\left((\nabla\cdot\nabla)\vec{d}+\frac{1}{1-2\nu} \nabla(\nabla\cdot\vec{d})\right)+\vec{f}_\mathrm{V}}$$

$$\rho\frac{\partial^2\vec{d}}{\partial t^2}.$$ = (4)

In equation (4), E denotes the modulus of elasticity, $\nu$ the Poisson's ratio, $\rho$ the density, $\vec{f}_\mathrm{V}$ the volume force and $\vec{d}$ the mechanical displacement.