Development of a macroscale constitutive model for porous magneto‐ active polymers using a computational homogenization approach

Over the last years there has been a growing interest in the study of the behavior of field‐responsive or so called smart materials. Porous magnetoactive polymers (MAPs) are a special class of these materials, where micron‐sized ferromagnetic particles are embedded into a porous crosslinked polymer matrix. Due to the mutual interaction of the particles upon magnetic stimulation, MAPs are able to deform and alter their effective material characteristics reversibly if subjected to a magnetic field. This strong magneto‐mechanical coupling makes them attractive for engineering applications e.g. in the field of sensors and actuators. The magneto‐mechanical behavior of porous MAPs is a complex phenomenon that spans over multiple length‐scales and essentially depends on (i) the constitutive behavior of the individual components, (ii) their morphology and microstructural arrangement and (iii) the macroscopic shape of the specimen. The strong shape effects pose a crucial challenge in the precise parameter identification of macroscopic models for MAPs based on experiments, see Keip & Rambausek [6] and Gebhart et al. [2, 3]. In order to circumvent these inherent problem, we propose a microscopic continuum‐based framework embedded into a suitable computational homogenization scheme to bridge between the micro‐ and macroscale, see Chatzigeorgiou et al. [1]. This modeling approach allows us to use much simpler constitutive models on the microscopic scale for which detailed and precise material parameters are available, see Kalina et al. [4, 5]. The proposed framework is then used to predict the effective macroscopic behavior of porous MAPs with random monodisperse microstructures. Based on the generated data set a thermodynamically consistent macroscale model for isotropic porous MAPs in an energy‐based constitutive setting is developed.