Effect of Magnetic Inclusions on the Effective Magnetostriction of Bulk Superconductors

A simple model is presented based on the Kim-Anderson model to further investigate the dependence of the effective magnetostriction of magnetic inclusion-superconducting matrix system on both the elastic and magnetic parameters including the elastic modulus, permeability, and volume fraction. The effect of the permeability on the magnetostriction is also obtained by implementing the continuity conditions of displacement and strain at the interface between the inclusion and the matrix through the magnetostriction loop. The results indicate that a stiffer inclusion can decrease the effective magnetostriction no matter whether the inclusion is magnetic or not and a larger effective magnetostriction can be obtained by choosing the matrix with a higher permeability, which gives an explanation about why the composite made from a matrix with a high permeability but a negligibly small magnetostriction yields unexpectedly low magnetostriction. Of particular interest is that in a certain range the effective magnetostriction of composites can be enhanced until it is saturated by increasing the permeability of matrix.