Snap buckling of bistable beams under combined mechanical and magnetic loading

Abstract

We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite-element modelling (FEM) and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel magnetization along the centreline, and is set into a bistable curved configuration by imposing an end-to-end shortening. Reversible snapping is possible between these two stable states. First, we experimentally characterize the critical field strength for the onset of snapping, at different levels of end-to-end shortening. Second, we perform three-dimensional FEM simulations using the Riks method to analyse high-order deformation modes during snapping. Third, we develop a reduced-order centreline-based beam theory to rationalize the observed magneto-elastic response. The theory and simulations are validated against experiments, with an excellent quantitative agreement. Finally, we consider the case of combined magnetic loading and poking force, examining how the applied field affects the bistability and quantifying the maximum load-bearing capacity. Our work provides a set of predictive tools for the rational design of one-dimensional, bistable, magneto-elastic structural elements. This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.

Foreword to the special issue on new developments in structural stability

“…Important time-dependent phenomena are identified and analysed in the paper such as delayed snapback and its dependence on the hold time prior to release of the load used to 'set' the buckle in the snapped state. Thus, this paper expands the scope of the papers by Lachmann et al [5] and Abassi et al [12] on elastic snap buckling of arched columns into the realm of shells with time-dependent material behaviour. The authors consider pressure and volume-change loadings of axisymmetric ellipsoidal shells with edge support conditions that give rise to snapping behaviour, and they focus their attention on the range of geometries for which the nonlinear buckling behaviour is axisymmetric.…”

“…The paper by Abassi et al . [ 12 ] provides design, analysis, and experimental testing of bistable compressed elastomeric columns driven from one stable state to the other by an external magnetic field that acts on magnetized particles that are embedded in the column. This paper serves as an exemplar of modern developments in stability theory.…”

“…[ 5 ] and Abassi et al . [ 12 ] on elastic snap buckling of arched columns into the realm of shells with time-dependent material behaviour. The authors consider pressure and volume-change loadings of axisymmetric ellipsoidal shells with edge support conditions that give rise to snapping behaviour, and they focus their attention on the range of geometries for which the nonlinear buckling behaviour is axisymmetric.…”

“…The last five papers in the special issue are illustrative of new applications involving buckling which bring to bear the analysis and experimental tools highlighted in this issue to design and explore the nonlinear buckling response of new structures. The paper by Abassi et al [12] provides design, analysis, and experimental testing of bistable compressed elastomeric columns driven from one stable state to the other by an external magnetic field that acts on magnetized particles that are embedded in the column. This paper serves as an exemplar of modern developments in stability theory.…”

Nonlinear Inflatable Actuators for Distributed Control in Soft Robots

“…Both effects cause a time delay between the pressure input and the deformation of the actuator such that the sequence depends on the timescale of the pressure input. [ 15,16,39 ] Another approach is to manufacture the actuators out of functional materials such that their thresholds can be tuned by external electric [ 40 ] or magnetic [ 41 ] fields. Finally, the snapping thresholds also depend on the external forces acting on each actuator (see Sections S3.3, S5.3, and S6.2, Supporting Information).…”