  We analyze the magnetostriction effect occurring in the magneto-sensitive
elastomers (MSEs) containing inhomogeneously magnetized particles. As it was
shown before, the expression for the interaction potential between two magnetic
spheres, that accounts for their mutual inhomogeneous magnetization, can be
obtained from the Laplace equation. We use this potential in the approximation
formula form to construct magnetic energy of the sample in terms of the
pairwise interactions of the particles. We show that this form of magnetic
energy leads to the same demagnetizing factor as predicted by the continuum
mechanics, confirming that only dipole-dipole magnetic interactions are
important on a large scale. As the next step, we examine the role played by the
particles arrangement on the magnetostriction effect. We consider different
spatial distributions of the magnetic particles: a uniform one, as well as
several lattice-type distributions (SC, BCC, HCP and FCC arrangements). We show
that the particles arrangement affects significantly the magnetostriction
effect if the separation between them became comparable with the particles'
dimensions. We also show that, typically, this contribution to the
magnetostriction effect is of the opposite sign to the one related with the
initial elastomer shape. Finally, we calculate the magnetostriction effect
using the same interaction potential but expressed in a form of a series
expansion, qualitatively confirming the above findings.
