Modeling and analysis of a magnetoelastic annular membrane placed in an azimuthal magnetic field

Abstract

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.

Structural instabilities in soft electro-magneto-elastic cylindrical membranes

“…In what follows, an asymptotic 2D theory for an electro-magneto-elastic membrane is derived starting from the 3D governing equations. The methodology used here is analogous to the work presented in Ali et al (2021).…”

“…2D magnetostatic governing equations of a membrane can be derived starting from the 3D magnetostatic equations (4) and jump conditions (9). Assuming that the magnetic field in free space is axially homogeneous, i.e., b + f = b − f = b f , the governing equations maybe derived as (Ali et al (2021))…”

“…This approach was extended by Saxena et al (2019); Reddy and Saxena (2018) to analyze the onset of snap-through point and wrinkling instabilities in a circular MRE membrane. More recently, Ali et al (2021) developed a 2D nonlinear magnetoelastic framework for annular magnetoelastic membranes deforming in the presence of azimuthal magnetic field.…”

Theoretical Modeling of Magnetoactive Elastomers on Different Scales: A State-of-the-Art Review

“…It was shown that the ratio of the magnetic constant to the elastic constant defines the deformation mode in the system under study. The work [ 89 ] developed the membrane theory for MAE-based devices. The asymptotic expansion of variational equations of 3D continuum theory was used to obtain an effectively two-dimensional theory of membrane deformation.…”

Modelling instabilities in electroelastic and magnetoelastic membranes: a very brief review

“…Choice of symmetric geometries allowed them to convert the resulting partial differential equations to ordinary differential equations. Ali et al (2021) derived a 2D membrane theory for magnetoelasticity using asymptotic analysis and studied the deformation of an annular membrane. Goulbourne et al (2007) derived the equilibrium equations and studied time-dependent response of a circular inflated electroelastic membrane.…”