Homogenization in magnetic-shape-memory polymer composites

TL;DR

This paper develops a homogenization-based model for magnetic-shape-memory polymer composites, enabling the prediction and optimization of their macroscopic behavior based on microstructure design.

Contribution

It introduces a variational homogenization model combining micromagnetism and elasticity for composite materials with periodic microstructure.

Findings

Numerical analysis of the cell problem reveals microstructure effects on macroscopic properties.

The model can be used to optimize particle shape and microstructure for desired behavior.

Homogenized model provides a practical tool for designing magnetic-shape-memory composites.

Abstract

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.