![]() ![]() 1b), a dilational material will strive to expel shear everywhere in favor of the dramatically softer dilational strains. While the elastic response of ordinary materials will locally be composed of some finite portion of shear (Fig. Here, we aim to decode the nonuniform deformations of metamaterials based on a dilational mechanism. ![]() d A fabricated sample of checkerboard material approximately preserves right angles (shown in yellow) under a generic nonlinear “foot” load, suggesting conformal deformation behavior. This angle-preserving behavior arises due to a local version of the RS mechanism, in which square elastic chunks of side length a rotate about small, flexible hinges of thickness ℓ to open and close pores according to α( x, y), the local linear dilation factor. c In contrast, a pure dilational metamaterial designed around the RS mechanism, may accommodate the loading without shearing of the unit cells, so that even as grid lines rotate, the angles between them remain fixed. b Applying fixed deformations (red arrows) at the boundary of a conventional elastic material leads to a spatially varying strain field that includes shear components that change the local angles between pieces of material, such as the initially perpendicular grid lines (blue, yellow). inhomogenous, loading conditions the response is more complex 17, and yet a general framework to describe the nonuniform soft deformations of mechanism-based metamaterials is lacking.Ī In the ideal rotating square mechanism, a structure of rigid squares (black) connected by frictionless hinges (red), may be dilated and contracted at zero energy cost when the squares are rotated opposite to their neighbors. While the dilational mechanism becomes a true zero energy motion in the limit of vanishing hinge size, for realistic metamaterials with finite hinges this uniform dilational motion is only observed for the particular case of a completely homogeneous loading condition. 1a) and has inspired the design of a range of metamaterials which collapse inward rather than bulge outward when compressed from the lateral direction 2, 15, 16. For example, the canonical rotating square (RS) mechanism, which consists of perfectly hinged rigid squares, enables a uniform dilational motion (Fig. Often these features rely on the careful arrangement of the cuts, pores and folds to emulate a mechanism, which is a special pathway of deformation that enables the metamaterial to change shape at a very small (ideally zero) energy cost. Mechanical metamaterials use patterns of cuts, pores and folds to achieve nonlinear 1, 2, 3, programmable 4, 5, polar 6, 7, 8 and other exotic behavior 9, 10, 11, 12, 13, 14 in response to external forcing.
0 Comments
Leave a Reply. |