Modeling of Magnetostriction of Soft Elastomer

Small magnetic particles placed in a relatively soft polymer (with elastic modulus E ~ 10-100 kPa) are magnetically soft elastomers. The external magnetic field acts on each particle which leads to microscopic deformation of the material and consequently to changing of its shape - magnetostriction. For purposes of studying of magnetostriction the model of movable cellular automata (MCA), in which a real heterogeneous material is an ensemble of interacting elements of finite size - automata, is used. It is supposed to be that the motion of each automata can be described by Newton's Second law. The force acting on the i-th automata consists of the following components: volume-dependent force acting on the automata i which is caused by pressure from the surrounding automata; force of an external magnetic field acting on the i-th automata with some magnetic moment; and normal and tangential interaction force between a pair of i and j automata. This approach was used for modeling of magnetostriction elastomer.