Performance enhancement of a magnetoactive elastomer actuator through a coupled magnetoelastic topology optimization scheme

We have found that considering local magnetic fields, large deformations, and magnetoelastic coupling simultaneously significantly affect the resulting shape in magnetoelastic topology optimization in a uniaxial actuator case. In contrast to the work presented here, other works incorporate magnetoelastic formulations that include simplifying assumptions on the local field, and subsequent effects on the magnetization response of the material, or the absence of large deformation mechanics, or both. These assumptions were shown to produce solutions that differ substantively from cases where local fields and large deformations are addressed concurrently. Magnetoelastic topology optimization schemes are needed to optimize magnetoactive elastomer (MAE) devices. MAE devices are magnetic particle_filled polymer matrices designed for specific actuations and controlled remotely by an external magnetic field. They garner considerable research interest as an emerging technology for actuators in soft robots or in applications requiring untethered actuation. The material properties of MAEs are dependent on the volume fraction of particles in the elastomer matrix, where a high-volume fraction increases relative permeability (for soft magnetic particles) but also increases elastic modulus. For optimal actuation, a tradeoff between low stiffness and high magnetic response must be made by adjusting volume fraction and controlling material placement. Using a topology optimization scheme that considers both the magnetic and mechanical properties of the material, the shape and material composition of the device can be tuned to best achieve the desired actuation displacement. In this work, a two-dimensional density-based magnetoelastic multimaterial topology optimization scheme for soft magnetic material is implemented in COMSOL Multiphysics. The optimization scheme uses multiphysics coupling that considers local magnetic fields and large deformations at each iteration through a Maxwell stress tensor formulation. A simulated example is then considered to demonstrate the effectiveness and necessity of a coupled optimization. The effect of considering large deformations during optimization is also investigated. It was found that a coupled topology optimization scheme with large deformations produced shapes with modes of actuation not captured by schemes with simplifying assumptions, leading to better performance at lower material cost. Considering large deformations in the coupled scheme offered significantly better performance, with an increase of 81.3% in a side-by-side performance simulation when compared to uncoupled cases.