Homogenization of 1D and 2D magnetoelastic lattices
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia
30332, United States
2 Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
* e-mail: email@example.com
Accepted: 17 November 2015
Published online: 26 January 2016
This paper investigates the equivalent in-plane mechanical properties of one dimensional (1D) and two dimensional (2D), periodic magneto-elastic lattices. A lumped parameter model describes the lattices using magnetic dipole moments in combination with axial and torsional springs. The homogenization procedure is applied to systems linearized about stable configurations, which are identified by minimizing potential energy. Simple algebraic expressions are derived for the properties of 1D structures. Results for 1D lattices show that a variety of stiffness changes are possible through reconfiguration, and that magnetization can either stiffen or soften a structure. Results for 2D hexagonal and re-entrant lattices show that both reconfigurations and magnetization have drastic effects on the mechanical properties of lattice structures. Lattices can be stiffened or softened and the Poisson’s ratio can be tuned. Furthermore for certain hexagonal lattices the sign of Poisson’s ratio can change by varying the lattice magnetization. In some cases presented, analytical and numerically estimated equivalent properties are validated through numerical simulations that also illustrate the unique characteristics of the investigated configurations.
Key words: Magneto-elastic / Homogenization / Tunable properties / Reconfiguration
© M. Schaeffer and M. Ruzzene, published by EDP Sciences, 2015
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.