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

secpiezo

## PiezoelectricityEdit

In the study of *piezoelectricity* ([#References|references]), on\index{piezo electricity}
the form chosen for is:

The tensor traduces a coupling between electrical field variables and the deformation variables present in the expression of :

The expression of becomes:

so:

## ViscosityEdit

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:

Material that obey such a law are called {\bf short memory materials} \index{memory} since the state of the constraints at time depends only on the deformation at this time and at times infinitely close to (as suggested by a Taylor development of the time derivative). Tensors and play respectively the role of elasticity and viscosity coefficients. If the strain-deformation relation is chosen to be:

eqmatmem

then the material is called *long memory* material since the state of the
constraints at time depends on the deformation at time but also on
deformations at times previous to .
The first term represents an instantaneous elastic effect. The second term
renders an account of the memory effects.

**Remark:**
Those materials belong ([#References

**Remark:**

In the frame of distribution theory, time derivatives can be considered as convolutions by derivatives of Dirac distribution. For instance, time derivation can be expressed by the convolution by . This allows to treat this case as a particular case of formula given by equation eqmatmem.