I want to know how we can relate magnetostriction with Applied magnetic field mathematically? Or if there is any way to derive it using mechanical equations?
Hi Dibyajyoti,
Strain = (Elastic Compliance * stress) + (piezomagnetic coupling * Magnetic field)
When stress is zero or constant, strain is proportional to magnetic field.
The piezomagnetic coupling is non-linear depending on stress and Mag field. However, it can be estimated by treating them linear.
The phenomenon of magnetostriction, a magnetoelastic effect, follows from energetic considerations: the coupling of the external magnetic field with the magnetisation in the system brings about a balance to be made between the magnetic energy associated with the magnetisation vector maintaining its equilibrium direction, and this vector undergoing a change in its direction with the attendant increase in the elastic deformation of the system. Magentostriction is a consequence of the latter energy increase being less than the former energy increase. For a modern review of the subject, consult the article by del Moral [1].
[1] A del Moral, Magnetostriction and Magnetoelasticity Theory: A Modern View, in Handbook of Magnetism and Advanced Magnetic Materials, Vol. 1, edited by H Kronmüller, and S Parkin (John Wiley & Sons, 2007). https://doi.org/10.1002/9780470022184.hmm114
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