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A theory of magneto-elastic nanorods obtained through rigorous dimension reduction

•We derive through a rigorous approach the 1D energy of a planar magnetic nanorod.•From the 1D energy we obtain the governing equilibrium equations and their linearized version.•We discuss an example of magneto-elastic buckling.•We provide a numerical comparison between the prediction of the 2D theo...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2022-06, Vol.106, p.426-447
Main Authors: Ciambella, Jacopo, Kružík, Martin, Tomassetti, Giuseppe
Format: Article
Language:English
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Summary:•We derive through a rigorous approach the 1D energy of a planar magnetic nanorod.•From the 1D energy we obtain the governing equilibrium equations and their linearized version.•We discuss an example of magneto-elastic buckling.•We provide a numerical comparison between the prediction of the 2D theory, used as starting point, and the 1D theory. Starting from a two-dimensional theory of magneto-elasticity for fiber-reinforced magnetic elastomers we carry out a rigorous dimension reduction to derive a rod model that describes a thin magneto-elastic strip undergoing planar deformations. The main features of the theory are the following: a magneto-elastic interaction energy that manifests itself through a distributed torque; a penalization term that prevents local interpenetration of matter; a regularization term that depends on the second gradient of the deformation and models microstructure-induced size effects. As an application, we consider a problem involving magnetically-induced buckling and we study how the intensity of the field at the onset of the instability increases if the length of the rod is decreased. Finally, we assess the accuracy of the deduced model by performing numerical simulations where we compare the two-dimensional and the one-dimensional theories in some special cases, and we observe excellent agreement.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2022.01.028