Magneto-active elastic shells with tunable buckling strength

Abstract

Shell buckling is central in many biological structures and advanced functional materials, even if, traditionally, this elastic instability has been regarded as a catastrophic phenomenon to be avoided for engineering structures. Either way, predicting critical buckling conditions remains a long-standing challenge. The subcritical nature of shell buckling imparts extreme sensitivity to material and geometric imperfections. Consequently, measured critical loads are inevitably lower than classic theoretical predictions. Here, we present a robust mechanism to dynamically tune the buckling strength of shells, exploiting the coupling between mechanics and magnetism. Our experiments on pressurized spherical shells made of a hard-magnetic elastomer demonstrate the tunability of their buckling pressure via magnetic actuation. We develop a theoretical model for thin magnetic elastic shells, which rationalizes the underlying mechanism, in excellent agreement with experiments. A dimensionless magneto-elastic buckling number is recognized as the key governing parameter, combining the geometric, mechanical, and magnetic properties of the system.

A comprehensive framework for hard-magnetic beams: reduced-order theory, 3D simulations, and experiments

“…The equilibrium equation is obtained using variational methods. Although performing the reduction from 3D to 1D is cumbersome compared to directly examining the equilibrium or energy of the beam centerline (Lum et al, 2016;Wang et al, 2020), this approach can serve as a starting point for modeling hard-magnetic structural elements with more complex geometries, such as rods (Chen et al, 2021b;Sano et al, 2021), plates, and shells (Yan et al, 2021). In parallel to the dimensionally reduced theory, we extend the framework for 3D hard-magnetic solids under a uniform field proposed by Zhao et al (2019) to the general case of an applied gradient field.…”

Instability caused swimming of ferromagnetic filaments in pulsed field

“…The bending modulus of the filament may be determined by the deformation of links 10 or the magnetic interaction of particles 11 – 13 . The buckling of magnetic rods and shells is studied in a series of works and we can mention just some of them 14 , 15 . The resultant deformation can be either an ‘S’ like shape, when the filament ends bend in the opposite direction or form a ‘U’ like shape 16 , 17 where the filament tangent at the center of the filament aligns with the field while its ‘arms’ move toward each other.…”

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

“…In particular, the geometry and placement of a dominant defect prescribe, respectively, the buckling strength and the spot where an instability localizes. Recent extensions of this concept couple geometric defects with differentially swelling [29] or magneto-responsive [30] materials to modify the knockdown factor over time. Relatedly, a more general study showed how a homogeneous natural curvature-which can be a proxy for nonmechanical stimuli like thermal expansion, changes in pH, or differential growth-acts to raise or lower the knockdown factor in spherical shells [31].…”