A unified numerical approach for soft to hard magneto-viscoelastically coupled polymers

The last decade has witnessed the emergence of magneto-active polymers (MAPs) as one of the most advanced multi-functional soft composites. Depending on the magnetisation mechanisms and responsive behaviour, MAPs are mainly classified as hard magnetic MAPs and soft magnetic MAPs. Polymeric materials are widely treated as fully incompressible solids that require special numerical treatment to solve the associated boundary value problem. Furthermore, both soft and hard magnetic particles-filled soft polymers are inherently viscoelastic. In this paper, we propose a unified simulation framework for magneto-mechanically coupled problems that can model hard and soft MAPs made of compressible and fully incompressible polymers, including the effects of the time-dependent viscoelastic behaviour of the underlying matrix. First, variational formulations for the uncoupled and coupled problems are derived. Later, the weak forms are discretised with higher-order Bézier elements while the evolution equation for internal variables is solved using the generalised-alpha scheme. Finally, using a series of experimentally-driven examples consisting of beam and robotic gripper models under magneto-mechanically coupled loading, the versatility and benefits of the proposed framework are demonstrated. The effect of viscoelastic material parameters on the response characteristics of MAPs under coupled magneto-mechanical loading is also studied