Introduction to Mathematical Physics/Energy in continuous media/Other phenomena

Piezoelectricity

In the study of piezoelectricity ([#References|references]), on\index{piezo electricity} the form chosen for ${\sigma }_{ij}$ is: Template:IMP/eq The tensor ${\gamma }_{ijk}$ traduces a coupling between electrical field variables $E_i$ and the deformation variables present in the expression of $F$: Template:IMP/eq The expression of $D_i$ becomes: Template:IMP/eq so: Template:IMP/eq

Viscosity

A material is called viscous \index{viscosity} each time the strains depend on the deformation speed. In the linear viscoelasticity theory ([#References|references]), the following strain-deformation relation is adopted: Template:IMP/eq Material that obey such a law are called {\bf short memory materials} \index{memory} since the state of the constraints at time $t$ depends only on the deformation at this time and at times infinitely close to $t$ (as suggested by a Taylor development of the time derivative). Tensors $a$ and $b$ play respectively the role of elasticity and viscosity coefficients. If the strain-deformation relation is chosen to be: Template:IMP/label Template:IMP/eq then the material is called long memory material since the state of the constraints at time $t$ depends on the deformation at time $t$ but also on deformations at times previous to $t$. The first term represents an instantaneous elastic effect. The second term renders an account of the memory effects. Template:IMP/rem Template:IMP/rem