Anisotropy in elastic modulus of hydrogel containing magnetic particles

We derive the analytic expression of elastic modulus for a gel containing magnetic particles with a magnetic dipole moment. The obtained elastic modulus is anisotropic and the modulus increases and decreases with the density of magnetic particle when the direction of strain is perpendicular and parallel to the direction of magnetization, respectively. This behavior is qualitatively in good agreement with previous experimental data [T. Mitsumata, et al., Macromol. Rapid Commun. 23, (2002) 178].