Modelling the curing process in magneto-sensitive polymers: Rate-dependence and shrinkage

• Curing reactions impart a continuous change of magneto-mechanical properties of iron-filled polymer composites.
• The hypoelastic constitutive relation can work under magnetomechanically coupled loads.
• The proposed model obeys the relevant laws of thermodynamics.
• The amount of curing-shrinkage is also dependent on the magnetic field during the curing process.

This paper deals with a phenomenologically motivated magneto-viscoelastic coupled finite strain framework for simulating the curing process of polymers under the application of a coupled magneto-mechanical load. Magneto-sensitive polymers are prepared by mixing micron-sized ferromagnetic particles in uncured polymers. Application of a magnetic field during the curing process causes the particles to align and form chain-like structures lending an overall anisotropy to the material. The polymer curing is a viscoelastic complex process where a transformation from fluid to solid occurs in the course of time. During curing, volume shrinkage also occurs due to the packing of polymer chains by chemical reactions. Such reactions impart a continuous change of magneto-mechanical properties that can be modelled by an appropriate constitutive relation where the temporal evolution of material parameters is considered. To model the shrinkage during curing, a magnetic-induction-dependent approach is proposed which is based on a multiplicative decomposition of the deformation gradient into a mechanical and a magnetic-induction-dependent volume shrinkage part. The proposed model obeys the relevant laws of thermodynamics. Numerical examples, based on a generalised Mooney–Rivlin energy function, are presented to demonstrate the model capacity in the case of a magneto-viscoelastically coupled load.