Magnetization and magnetostriction curves from micromagnetics

The macroscopic behavior of magnetostrictive materials results from domain evolutions, often occurring at a microscopic scale. It is shown how to compute magnetization and magnetostriction curves by appraising the behavior of the underlying microstructures. The method hinges on an averaging device (Young measures), which allows one to pass from the microscopic to the macroscopic scale. The kinematical constraints on the accommodation of elastic effects are taken into account, and the role of material symmetry in the selection of energetically optimal microstructures is highlighted. Moreover, the effect of magnetoelastic coupling on the computation of magnetization curves is discussed.