Modeling and Simulation of Magnetic Shape--Memory Polymer Composites

Composites of small magnetic-shape-memory (MSM) particles embedded in a polymer matrix have been proposed as an energy damping mechanism and as actuators. Compared to a single crystal bulk material, the production is simpler and more flexible, as both type of the polymer and geometry of the microstructure can be tuned. Compared to polycrystals, in composites the soft polymer matrix permits the active grains to deform to some extent independently; in particular the rigidity of grain boundaries arising from incompatible orientation is reduced. We study the magnetic-field-induced deformation of composites, on the basis of a continuous model incorporating elasticity and micromagnetism, in a reduced two-dimensional, plane strain setting. The aim is to give conceptual guidance for the design of composite materials independent of the concrete macroscopic device. Thus on the background of homogenization theory, we determine the macroscopic behaviour by studying an affine-periodic cell problem. An energy descent algorithm is developed, whose main ingredients are a boundary element method for the computation of the elastic and magnetic field energies; and a combinatorial component reflecting the phase transition in the individual particles, which are assumed to be of single–domain type. Our numerical results demonstrate the behavior of the macroscopic material properties for different possible microstructures, and give suggestions for the optimization of the composite.