A phantom-chain based viscoplastic model for local relaxation of magneto-active polymer composites under dynamic magnetic field

Magneto-active polymer composites (MAPCs) can change their mechanical properties (i.e., stiffness) and/or mechanical deformation upon an external magnetic stimulus. The mechanical response of MAPCs is primarily determined by the interaction between the polymer matrix and magnetic particles, alongside the performance of the constituent materials. When a directional dynamic magnetic field is applied, mainly two types of relaxation behavior occur due to magnetic particle oscillations and rotations, i.e., heat-generation caused phase change and viscosity reduction, and chain cleavage and de-adhesion from particles. This material relaxation caused by local chain debonding is fundamentally different from that by the phase transition characterized with variation of free volumes. This work proposes a phantom-chain based magnetomechanical model to reflect magnetic particles oscillating caused local material relaxation, and a Maxwell rheological model is superimposed to capture the heat-triggered relaxation behavior of MAPCs under dynamic magnetic field. Considering changes in the chain configuration, a phantom-chain model is constructed by wave-propagation modeling and further integrated through full network space to capture the overall magnetomechanical properties of MAPCs. The magnetic field triggered heat-generation is simulated by both Brownian relaxation and Neel relaxation. The model is calibrated through a series of tests and then applied in simulations of the isothermal uniaxial tension of MAPCs, both with and without external magnetic fields. These simulations show the model's effectiveness in capturing the material relaxation behavior of MAPCs under dynamic magnetic activation. Good agreement between the simulations and experiments demonstrates the validation and effectiveness of the proposed model and solution procedure. The calibrated model is further applied to the multi-cycle shape memory modeling of MAPCs under the alternating magnetic field. This work lays a theoretical foundation and contributes to the design and widespread application of 3D complex microstructured MAPCs.