Analysis and Modeling of Magnetoelastic Circular Membrane

In the present work, a nonlinear 2D magnetoelastic membrane formulation is derived 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 discussed by [29]. A weakly magnetizable material's asymptotic O(h) membrane theory is developed by expanding the governing equations of the 3D magnetoelastic theory. The present formulation is developed considering a strain energy function dependent on the deformation gradient F and magnetic field H. The model is applied to a circular geometry of the membrane. The 2D governing equations are reduced to a system of ordinary differential equations (ODEs) by specializing in axisymmetry andconsidering combined magnetoelastic loading. The varying magnetic field and transverse inputs are used to conduct parametric investigations, and the results are validated with the past research.