Bi-stiffness property of motion structures transformed into square cells

Abstract

Cellular solids with internal microstructures enable the reduction in some environmental loads because of their lightweight bodies, and deliver unique elastic, electromagnetic and thermal properties. In particular, their large deformability without topological change is one of their most interesting solid properties. In this study, we propose a bar-and-joint framework assembled with a basic unit of motion structure, which has eightfold rotational symmetry (MS-8). The MS-8 is made of tetragons, arranged in a concentric fashion, which are transformed into either one of two different aligned patterns of square cells according to the coordinated rotations of the inside squares. Square cells are extremely anisotropic, which is why the stiffness of the MS-8 changes dramatically in the transformation process. Thus, the MS-8 exhibits bi-stiffness according to the two different motions. Taking advantage of the bi-stiffness property, the possibilities of deformation behaviours for repetitive structures of MS-8s are discussed.

Orthotropic Laminated Open-cell Frameworks Retaining Strong Auxeticity under Large Uniaxial Loading

“…For example, an array of rotating rigid units can induce auxetic behavior, and this is one of the fundamental auxetic mechanisms according to some background on geometry3031323334353637. Many auxetic cellular and laminated composite solids can be designed from considerations of geometry and rotation3738394041424344.…”

Transition mechanism for a periodic bar-and-joint framework with limited degrees of freedom controlled by uniaxial load and internal stiffness

“…In this context, our previous study proposed a cellular structure with unique connectivity and eightfold rotational symmetry [ 54 ]. Depending on the direction of uniaxial loading, this structural system undergoes two types of kinematic transformations, diamond- and square-patterned unit cells [ 55 ], here termed Pattern-D and Pattern-S, respectively. Controlling the point of loading enables the structure to switch between these two motions.…”

Switching between two types of auxetic behavior of two-dimensional periodic cells with square rotation

“…We assume all cell walls are rigid and represent them as bars , then we weld couples of bars of the same color and pin couples of bars of different color. The bar‐and‐joint framework has a single degree of freedom and its transformations are divided into Motions I and II (). While it is obvious that because the two motions are orthogonally equivalent, we here formally derive the Poisson's ratio of the structure according to the methodology of material mechanics .…”

“…Two transformations of the proposed system (): (a) Motion I and (b) Motion II. The purple bars indicate complete overlaps between the red and blue bars.…”

“…Applying the total Lagrangian formulation to our flexibly jointed modeling with finite beam elements [10,46,49], we performed large-deformation analyses of the proposed model with a change in k. As the numerical procedure, we adopted the arc-length method [50], which allows us to overcome local minimum and maximum points of the equilibrium path that we should solve. Figure 5a shows the calculated stress-…”