A geometrically exact model for thin magneto-elastic shells. (September 2022)

• Record Type: Journal Article
• Authors: Pezzulla, Matteo; Yan, Dong; Reis, Pedro M.
• Is Part Of: Journal of the mechanics and physics of solids. Volume 166(2022)
• Publication Date: 2022-09
• Subjects: Magneto-rheological elastomers -- Slender structures -- Shells -- Buckling; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2022.104916
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff–Love assumption, we derive a reduced two-dimensional magneto-elastic energy that can be minimized through numerical analysis. In parallel, we simplify the reduced energy by expanding it up to the second order in the displacement field and provide a physical interpretation. Our theoretical analysis allows us to identify and interpret the two primary mechanisms dictating the magneto-elastic response: a combination of equivalent magnetic pressure and forces at the first order, and distributed magnetic torques at the second order. We contrast our reduced framework against a three-dimensional nonlinear model by investigating three test cases involving the indentation and the pressure buckling of shells under magnetic loading. We find excellent agreement between the two approaches, thereby verifying our reduced model for shells undergoing nonlinear and non-axisymmetric deformations. We believe that our model for magneto-elastic shells will serve as a valuable tool for the rational design of magnetic structures, enriching the set of reduced magnetic models. Highlights: We derive a geometrically exact model for magneto-active shells undergoing 3D deformation. The reduced magnetic energy is interpreted as the energy potential of magnetic forces and torques. Our analysis provides an understanding of the magneto-elastic coupling for curved geometries. We contrast the results from our theory with 3D FEM to test the model. The reduced 2D model is ten times faster than its 3D counterpart.