Homogenization in magnetic-shape-memory polymer composites
This work provides a theoretical and numerical framework for designing polymer composites that mimic single-crystal magnetic-shape-memory alloys, addressing manufacturing challenges for engineers and materials scientists.
The authors developed a variational model for magnetic-shape-memory polymer composites and derived an effective macroscopic model via homogenization under periodic microstructure assumptions. Numerical simulations of the cell problem show how microstructure geometry affects macroscopic behavior, enabling optimization of particle shape and arrangement.
Magnetic-shape-memory materials (e.g. specific NiMnGa alloys) react with a large change of shape to the presence of an external magnetic field. As an alternative for the difficult to manifacture single crystal of these alloys we study composite materials in which small magnetic-shape-memory particles are embedded in a polymer matrix. The macroscopic properties of the composite depend strongly on the geometry of the microstructure and on the characteristics of the particles and the polymer. We present a variational model based on micromagnetism and elasticity, and derive via homogenization an effective macroscopic model under the assumption that the microstructure is periodic. We then study numerically the resulting cell problem, and discuss the effect of the microstructure on the macroscopic material behavior. Our results may be used to optimize the shape of the particles and the microstructure.