This work presents the development of a 2D nonlinear magnetoelastic framework for a thin membrane undergoing large deformations. An asymptotic [Formula: see text] theory is obtained, starting from the 3D variational magnetostatic and force balance equations for a weakly magnetizable material, using the approach described by Steigmann. The model is subsequently specialized to axisymmetry and applied to a pre-stretched annular membrane deforming under azimuthal magnetic field and transverse pressure loading. Parametric studies are performed by varying the pre-stretch, magnetic field, and transverse pressure inputs.

This paper presents a computationally efficient constitutive model for magnetostrictive materials. High computational efficiency is achieved through the use of local linearization (about easy axes) and discrete energy-averaging techniques. The model is applied to iron-gallium alloys (Galfenol) and tested for different magnetic field orientations relative to the easy axes. It is observed that the model accurately predicts both sensing and actuation characteristics while reducing the computation time by a large factor (.1000 times) when compared to the nonlinear energy minimization models. Furthermore, the average error observed in λ-H and B-H curves is less than 3.5% with the error increasing at magnetic field orientations farther from easy axes, particularly at large magnetic field values. Finally, the model is integrated with a finite element framework to predict the response of a Galfenol rod transducer system, and parametric studies are performed for different current and prestress conditions to optimize the device performance.

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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 placed 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. Application of electric field, on the other hand, results in an early onset of limit-point instability (i.e., at smaller stretches) compared to the hyperelastic case. Additionally, electrical limit-point instability, characterized by a loss of monotonicity in voltage versus stretch plots, is observed and its dependence on magnetic field and force inputs is studied. 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 fields inputs. In summary, our membrane model describes the interactions between the electromagnetic fields and deformation in a soft functional material, and can be applied towards design of soft actuator and sensor devices.