Magnetostrictive solids: macroscopic response and microstructure evolution under applied magnetic fields and loads

The macroscopic behavior of magnetostrictive materials results from domain evolutions occurring at a microscopic scale. We show how to compute virgin magnetization and magnetostriction curves by appraising the behavior of the underlying microstructures. Our method hinges on an averaging device (Young measures), which allows us to pass from the microscopic to the macroscopic scale. We take into account the kinematical constraints on the accommodation of elastic effects, and we highlight the role of material symmetry in the selection of energetically optimal microstructures. Finally, we analyze the influence of applied surface tractions on the magnetoelastic response of a magnetostrictive specimen.