The magnetoelastic energy describes the energy storage due to elastic lattice distortions. It may be neglected if magnetoelastic coupled effects are neglected.
There exists a preferred local distortion of the crystalline solid associated with the magnetization director m, . 
For a simple model, one can assume this strain to be isochoric and fully
isotropic in the lateral direction, yielding the deviatoric ansatz
where the material parameter E > 0 is the magnetostrictive
constant. Clearly, E is the strain induced by the magnetization in
the direction m. With this ansatz at hand, we consider the elastic
energy density to be a function of the elastic, stress-producing
strains . A quadratic form for the magnetoelastic energy is
where 
is the fourth-order elasticity tensor. Here the elastic response is assumed to be isotropic (based on 
the two Lamé constants λ and μ).
Taking into account the constant length of m, we obtain the invariant-based representation
This energy term contributes to magnetostriction.