Magnetorheological elastomers (MREs) are a new class of smart materials that can change their mechanical properties in the presence of an external magnetic field. These materials have a wide range of applications in inflatable terrestrial and space structures, dampers, biological membranes, shock absorbers, sensors, and actuators, etc [1- 4]. Therefore, it becomes essential to develop computationally efficient nonlinear coupled magnetoelastic models to enable the design and optimization of MRE-based devices. Development of asymptotic 1D or 2D models can further reduce the computational cost.&nbsp;In the present work, a nonlinear 2D magnetoelastic membrane formulation is presented starting from the 3D governing equations. To have empirical access to a wide range of strain space, a two-dimensional approximation to the three-dimensional boundary value problem has been derived using the membrane formulation developed by discussed by Steigmann [5]. An asymptotic O(h) membrane theory is derived through an asymptotic expansion of 3D magnetoelastic governing equations, for a weakly magnetizable material. The present formulation is developed considering a strain energy function dependent on deformation gradient and magnetic field. The model is applied to two different membrane geometries: cylindrical and circular. The 2D governing equations are reduced to a system of ordinary differential equations (ODEs) by specializing to axisymmetry and considering combined magnetoelastic loading. Our membrane theory is validated with the existing literature, for the special case of a hyperelastic, Neo-Hookean membrane under transverse pressure loading, in the absence of an external magnetic field. The deformation of the magnetoelastic membrane is subsequently analyzed in the presence of an external magnetic field in different directions for both circular and cylindrical geometries. The resulting system of nonlinear ODEs is non-dimensionalized and solved computationally using MATLAB boundary value (bvp) problem. The deformation is analyzed for isotropic, incompressible magnetoelastic membranes for different boundary conditions and material models. Instability in deformation was observed after a certain value of pressure and magnetic field inputs. Parametric studies are further performed to enhance actuator performance by varying transverse pressure and magnetic field inputs.&nbsp;&nbsp;References&nbsp;1.&nbsp;&nbsp;&nbsp; Bira, Nicholas, Pallavi Dhagat, and Joseph R. Davidson. "A Review of Magnetic Elastomers and Their Role in Soft Robotics."&nbsp;Frontiers in Robotics and AI&nbsp;7 (2020): 146.2.&nbsp;&nbsp;&nbsp; Bica, I., and E. M. Anitas. "Magnetodielectric effects in membranes based on magnetorheological bio-suspensions."&nbsp;Materials &amp; Design&nbsp;155 (2018): 317-324.3.&nbsp;&nbsp;&nbsp; Mikhailov, Valery P., and Alexey M. Bazinenkov. "Active vibration isolation platform on the base of magnetorheological elastomers."&nbsp;Journal of Magnetism and Magnetic Materials&nbsp;431 (2017): 266-268.4.&nbsp;&nbsp;&nbsp; Lee, Mina, Taewoong Park, Chaemin Kim, and Sung-Min Park. "Characterization of a magneto-active membrane actuator comprising hard magnetic particles with varying crosslinking degrees."&nbsp;Materials &amp; Design&nbsp;195 (2020): 108921.5.&nbsp;&nbsp;&nbsp; Steigmann, David J.&nbsp;Finite elasticity theory. Oxford University Press, 2017.

Axisymmetric Nonlinear Deformation of Magnetoelastic Membranes

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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