Coupled magnetic field and viscoelasticity of ferrogel

Composed of a soft polymer matrix and magnetic filler particles, ferrogel is a smart material responsive to magnetic fields. Due to the viscoelasticity of the matrix, the behaviors of ferrogel are usually rate-dependent. Very few models with coupled magnetic field and viscoelasticity exist in the literature, and even fewer are capable of reliable predictions. Based on the principles of nonequilibrium thermodynamics, a field theory is developed to describe the magneto-viscoelastic property of ferrogel. The theory provides a guideline for experimental characterizations and structural designs of ferrogel-based devices. A specific material model is then selected and the theory is implemented in a finite-element code. As numerical examples, the responses of a ferrogel in uniform and non-uniform magnetic fields are analyzed. The dynamic response of a ferrogel to cyclic magnetic fields is also studied, and the prediction agrees with our experimental results. In the reversible limit, our theory recovers existing models for elastic ferrogel, and is capable of capturing some instability phenomena.