Homogenization and multiscale stability analysis in finite magneto‐electro‐elasticity

Abstract

AbstractSoft matter electro‐elastic, magneto‐elastic and magneto‐electro‐elastic composites exhibit coupled material behavior at large strains. Examples are electro‐active polymers and magnetorheological elastomers, which respond by a deformation to applied electric or magnetic fields, and are used in advanced industrial environments as sensors and actuators. Polymer‐based magneto‐electric‐elastic composites are a new class of tailor‐made materials with promising future applications. Here, a magneto‐electric coupling effect is achieved as a homogenized macro‐response of the composite with electro‐active and magneto‐active constituents. These soft composite materials show different types of instability phenomena, which even might be exploited for future enhancement of their performance. This covers micro‐structural instabilities, such as buckling of micro‐fibers or particles, as well as material instabilities in the form of limit‐points in the local constitutive response. Here, the homogenization‐based scale bridging links long wavelength micro‐structural instabilities to material instabilities at the macro‐scale. This work outlines a framework of an energy‐based homogenization in electro‐magneto‐mechanics, which allows a tracking of postcritical solution paths such as those related to pull‐in instabilities. Representative simulations demonstrate a tracking of inhomogenous composites, showing the development of postcritical zones in the microstructure and a possible instable homogenized material response. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)