DEFORMATION OF A MAGNETIC ELASTOMER WITH ALLOWANCE FOR MAGNETO-INDUCED STRUCTURE FORMATON

Abstract

In this work a numerical scheme is presented that enables one to calculate in detail a quasi-static deformation of a SME sample containing up to several tens of particles. The algorithm is organized as follows. First for the sample of a given shape by the finite element method under given boundary conditions the linear response tensor L is evaluated, which connects together the displacements of the sample boundaries and the particles inside it for a given distribution of the applied forces. The energy of the sample is composed as a sum of the elastic (evaluated with the help of L) and magnetic parts. This function is then minimized for each value of the applied field under assumptions of incompressibility of the matrix and non-overlapping of the particles. By that, the equilibrium values of the particle displacements and the sample boundary deformations are determined. The developed approach is stable even under substantial structure changes. As an example, a SME sample containing 64 particles is considered. Its stress-strain curves for different values of the applied field and the field dependence of the elastic modulus are presented.