Frictional Effects in Biomimetic Scales Engagement

Scales engagement can contribute significantly to nonlinear bending behavior of elastic substrates with rigid biomimetic scales. In this letter, we investigate the role of friction in modulating the nonlinearity that arises due to self-contact of scales through an analytical investigation. We model the friction as dry Coulomb type friction between rigid links and the substrate is taken to be linear elastic. Our results reveal that frictional effects give rise to two possible locking mechanisms, namely static friction lock and kinetic friction lock. These locks arise due to a combination of interfacial behavior and geometry. In addition to these extremes, the frictional behavior is found to increase stiffness of the structure. This dual nature of friction which influences both system operation and its terminal limit results in the maximum relative frictional work to lie at intermediate friction coefficients and not at the extremes of frictional limits.Comment: 4 pages, 4 figure

Wrinkling reveals a new isometry of pressurized elastic shells

We consider the point indentation of a pressurized, spherical elastic shell. Previously it was shown that such shells wrinkle once the indentation reaches a threshold value. Here, we study the behaviour of this system beyond the onset of instability. We show that rather than simply approaching the classical `mirror-buckled' shape, the wrinkled shell approaches a new, universal shape that reflects a nontrivial type of isometry. For a given indentation depth, this ``asymptotic isometry", which is only made possible by wrinkling, is reached in the doubly asymptotic limit of weak pressure and vanishing shell thickness.Comment: 6 pages main text plus 14 pages of supplementary informatio

Mechanical properties and energy absorption of heterogeneous and functionally graded cellular structures

AbstractThe crushing behaviour and energy absorption of honeycombs made of a linear elastic-perfectly plastic material with constant and functionally graded density were studied up to large crushing strains using finite element simulation. Our numerical simulations showed three distinct crushing modes for honeycombs with a constant relative density: quasi-static, transition and dynamic. Moreover, irregular cellular structures showed to have energy absorption similar to their counterpart regular honeycombs of same relative density and mass. To study the dynamic crushing of functionally graded cellular structures, a relative density gradient in the direction of crushing was introduced in the computational models by a gradual change of the cell wall thickness. Decreasing the relative density in the direction of crushing was shown to enhance the energy absorption of honeycombs at early stages of crushing. We also developed detailed finite element models of a three-dimensional closed-cell rhombic dodecahedron structure subjected to dynamic crushing. We specifically quantified the distribution of plastic strain and energy absorption of the cellular structure and provided a comparison with the results obtained in analysis of 2-D cellular structures. The results provide new insight into the behavior of engineered and biological cellular materials, and could be used in development of a new class of energy absorbent cellular structures

Slender Origami with Complex 3D Folding Shapes

One-dimensional slender bodies can be deformed or shaped into spatially complex curves relatively easily due to their inherent compliance. However, traditional methods of fabricating complex spatial shapes are cumbersome, prone to error accumulation and not amenable to elegant programmability. In this letter, we introduce a one-dimensional origami based on attaching Miura-ori that can fold into various programmed two or three-dimensional shapes. We study the out-of-plane displacement characteristics of this origami and demonstrate with examples, design of slender bodies that conform to programmed complex spatial curves. Our study provides a new, accurate, and single actuation solution of shape programmability

Real-time reversible tunable elasticity in cellular solids via electromagnetic actuation

The ability for reversible, real-time control of elastic moduli in solids can find significant application in advanced mechanical components, protective structures, and biomedical devices. Here, we propose a novel concept for controlling the linear and nonlinear elastic properties of cellular structures via electromagnetically triggered mechanisms in the cellular solid. Three structural systems with orthotropic material properties were proposed and studied numerically, experimentally, and analytically. Using the proposed concept, the elastic modulus can be controlled over two to four orders of magnitude. The Poisson ratio of the isotropic structure can be varied from 0 to 0.5 continuously. The adjustments over nonlinear elastic (i.e., buckling) behavior of the structure are achieved by activation of supplementary cell walls in the lattice through electromagnetic actuation. Magnetic actuation will hamper the first symmetrical buckling pattern of the structure and force the structure to buckle according to a higher buckling pattern with smaller sinusoidal wavelength in the cell walls. The uniaxial buckling strength of the structure was tuned over two orders of magnitude

Mechanics of elastic ellipsoidal shells

Complicated structural features at a much smaller scale than overall structure size form during the deformation of elastic shells under mechanical loading. These features which can be seen by simple experiments in everyday life, as well as in biological and engineering systems, are associated with high energy density and evolve in intricate ways as the shell is further loaded deep into the nonlinear regime. The key challenge in understanding these features is interaction of physics and geometry that leads to a mechanical response which is very different from the response of solid objects. The formation of localized periodic structures in the crushing of a spherical shell, such as a ping pong ball, is well documented in the literature and studies show that spherical shells manifest periodic structures as polygons under point and plate loading. We studied ellipsoidal shells under plate and point indentation and results are presented here. For plate indentation, we present a new instability that is observed in the indentation of a highly ellipsoidal shell. In this phenomenon, above a critical indentation depth, the plate loses contact with the shell in a series of well-defined “blisters” aligned with the smaller radius of curvature. We used detailed numerical model to study this instability and explained it using scaling arguments. We characterized the onset of instability and showed relation between number of blisters and their sizes with indentation depth and geometry of shell. Our study showed that properties of blister are independent of elastic properties of shell itself and this suggests a novel method for simply determining the thickness of highly ellipsoidal shells