Structural instabilities in soft electro-magneto-elastic cylindrical membranes

Abstract

In the present work, a nonlinear coupled electro-magneto-elastic membrane formulation is developed for soft functional materials starting from the variational form of 3D governing equations. The resulting 2D model is applied to an internally pressurized cylindrical membrane in an azimuthal magnetic field and radial electric field. The results of our model are verified with existing literature for some special cases. The model is subsequently used to analyze mechanical and electrical limit-point instabilities and the effect of external fields on the onset of these instabilities. It is observed that the onset of mechanical limit-point instability, defined by a loss of monotonicity in the pressure versus deformation plots, is dependent on the material properties, geometrical parameters, and applied electromagnetic fields. Magnetic field-induced instability results in an initial dip in the pressure versus stretch plots, subsequently converging to the purely hyperelastic membrane behavior at larger stretches. On the other hand, applying an electric field results in an early onset of limit-point instability (i.e., at smaller stretches) compared to the hyperelastic case. In this work, we additionally observe the presence of an electrical limit-point instability, characterized by a loss of monotonicity in voltage versus stretch plots. The dependence of electrical-limit point on magnetic field and force inputs is studied. To the best of our knowledge, this effect has not been discussed in prior literature. Finally, we study the effect of Maxwell stress due to electromagnetic fields. It is observed that ignoring the Maxwell stress related traction boundary term results in an error of up to 10%, depending on the force and magnetic field inputs. In summary, our membrane model describes the interactions between the electromagnetic fields. The electric, magnetic and elastic limit points observed in these membranes under different set of loading conditions can be used towards improving the design of soft actuator and energy-harvesting devices.