A multi-scale approach to model the curing process in magneto-sensitive polymeric materials

We propose a magneto-mechanically coupled multi-scale model for simulating the curing process of polymers. In the case of magneto-sensitive polymers, micron-size ferromagnetic particles are mixed with a liquid polymeric matrix in the uncured stage. The polymer curing process is a complex process that transforms a fluid to a solid with time. To transfer the constituent parameter information from the micro-scale to the macro-scale for a composite magneto-mechanically coupled polymeric material, an extended Mori-Tanaka semi-analytic homogenization procedure is utilized. The stiffness gaining phenomenon as in the case of a curing process is realized by time-dependent material parameters appearing within the composite piezomagnetic material tensors. Moreover, to compute the volume reduction during curing, a magnetic induction dependent shrinkage model is proposed. Several numerical examples show that the model proposed herein can capture major observable phenomena in the curing process of polymers under magneto-mechanically coupled infinitesimal deformations.