Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures

Abstract

Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells.

Shape selection and multi-stability in helical ribbons

“…6 To obtain the values of j 1 , j 2 , and /, we employ a theoretical model based on linear elasticity theory, differential geometry, and stationarity principles, which takes into consideration both the non-uniform bending and mid-plane stretching due to geometric nonlinearity. 3,43 We have shown 4,6 that it is sufficient to consider the case when the ribbon is only subjected to an effective surface stress on the bottom surface, f à ¼ f 1 r 1 r 1 þ f 2 r 2 r 2 . Here, we assume the materials are isotropic and linear elastic, with Young's modulus E and Poisson's ratio .…”

“…3,43 When g W ffiffiffiffiffiffiffiffiffi 43 we get a characteristic width W 0 % 2:5 ffiffiffiffiffiffiffiffiffi H=j p (where j maxfjj 1 j; jj 2 jg). Since j is unknown, we use an equivalent parameter,…”

Geometrically controlled snapping transitions in shells with curved creases

“…For example, Venus flytraps (Dionaea muscipula) use this mechanism to generate a snapping motion to close their leaves (11), hummingbirds (Aves: Trochilidae) twist and rotate their curved beaks to catch insect prey (14), and engineered microlenses use a combination of bending and stretching energy to rapidly switch from convex to concave shapes to tune their optical properties (12). Despite the ability to engineer bistability and snapping transitions in a variety of systems by using prestress or material anisotropy (18)(19)(20)(21)(22)(23)(24), a general geometric design rule for creating a snap between stable states of arbitrary surfaces does not exist. This stands in stark contrast to the well-known rules and consequences for folding of a flat sheet, as shown in origami design (25)(26)(27).…”

Exploiting the instability of smart structure for reconfiguration

“…24 Furthermore, an advanced application has been investigated to synthesise the multistability by connecting bistable units together. 25 Nonlinear behaviour in mechanical multistable structures related with bifurcation phenomena 26 and some key parameters could be proposed to switch between different functional configurations upon actuation. 27 In general, nonlinear dynamical systems typically possess a number of equilibria which are stable and unstable.…”