Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers

Iron-filled magnetorheological polymers, when cured in the presence of a magnetic field, result in having a transversely isotropic structure with iron particles forming chains along the direction of applied magnetic induction. In this work, we model the magneto-viscoelastic deformation (and magnetization) process of such polymers. Components of the deformation gradient and the applied magnetic induction in the direction of anisotropy are considered to be additional arguments of the energy density function. The existence of internal damping mechanisms is considered by performing a multiplicative decomposition of the deformation gradient and an additive decomposition of the magnetic induction into equilibrium and non-equilibrium parts. Energy density functions and evolution laws of the internal variables are proposed that agree with the laws of thermodynamics. In the end, we present solutions of some standard deformation cases to illustrate the theory. In particular, it is shown that the orientation of resultant magnetic field and principal stress directions change with time owing to viscoelastic evolution.