Tailorable elasticity of cantilever using spatio-angular functionally graded biomimetic scales

Abstract

Cantilevered beams are of immense importance as structural and sensorial members for a number of applications. Endowing tailorable elasticity can have wide ranging engineering ramification. Such tailorability could be possible using some type of spatial gradation in the beams material or cross section. However, these often require extensive additive and subtractive material processing or specialized casts. In this letter, we demonstrate an alternative bio inspired mechanical pathway, which is based on exploiting the nonlinearity that would arise from a functionally graded distribution of biomimetic scales on the surface using an analytical approach. This functional gradation is geometrically sourced and could arise from either spatial or angular gradation of scales. We analyze such a functionally graded cantilever beam under uniform loading. In comparison with uniformly distributed scales, we find significant differences in bending stiffness for both spatial and angular gradations. Spatial and angular functional gradation share some universality but also sharp contrasts in their effect on the underlying beam. A combination of both types of gradation in the structure can be used to alternatively increase or decrease stiffness and therefore a pathway to tailor the elasticity of a cantilever beam relatively easily. These results give rise to an architected framework for designing and optimizing the topography of leveraged solids.Cantilevered beams arise in a number of diverse engineering applications spanning an enormous variety of length scales [1,2,3,4,5,6,7,8,9,10]. In several of these applications, tailoring elasticity can be of tremendous significance since it can be used to design the response according to stimulus or guard against unwanted instabilities.To this end, functional gradation (FG) is a useful strategy. FG materials are high performance composite materials consisting of two or more constituent phases with variegation in composition. This gradation can lead to a desired enhancement in the thermal/mechanical properties, compared to their conventional counterparts. This makes them ideal for various engineering applications including biomedical [11,12], cellular structures [13,14,15,16,17,18], soft robotics [19,20] and several others [21,22].However, typical FG materials could be difficult to fabricate requiring extensive materials processing such as directional solidification [23], specialized machining paths or even additive manufacturing [23,24]. An alternative exists in pursuing surface based strategy such as biomimetic scales. Such dermal scales are a pervasive feature within Kingdom Animalia. Their advantages extend well into a variety of important functions, which enhance survivability, such as protection, camouflaging, and locomotion [25,26,27,28,29]. In nature, certain fishes possess remarkably periodic scale distribution, for instance, Elasmobranchs [30,31] and Teleosts [32,33,34,35]. However, more often, organisms display a large variation in scale distribution within their own bodies [36,37,...

Bending behavior of biomimetic scale covered beam with tunable stiffness scales

“…The parameters affecting the bending deformation modes are relative stiffnesses of the scales and the substrate, scales overlap ratios, length, contact friction and some other geometrical parameters discussed in previous studies [16][17][18] . These nonlinear regimes are more universal than pure bending and also reported in non-uniform loads as well as torsion 16,19,20 . Thus clearly, changing the scales properties can lead to a change in the overall behavior of the structure.…”

Coupled Bend-Twist Mechanics of Biomimetic Scale Substrate

“…The essential characteristics of bending behavior such as strain stiffening and locked states were found to be universally valid even when stiff scales were not uniformly distributed (e.g. functionally graded [18]) or loaded under non-uniform bending [17]. The locked state is essentially a kinematic configuration beyond with scale motion would result in interpenetration leading to rigid behavior.…”

“…This makes K independent of s and helps set up periodicity conditions to extract structureproperty relationships. For sharp gradients in strains or functionally graded structures, either local periodicity [18] or discrete scale by scale approach can be used [17]. The periodicity condition allows us to study the kinematics using a representative volume element (RVE) of a pair of scales [14,25].…”

“…In addition, the assumption of periodicity of contact (i.e., the use of RVEs) is also common [14,21]. Non-periodic or functionally graded systems have been investigated previously for the cases of pure bending and pure twisting and have indicated the salient features of these systems are still preserved under periodicity [17,18]. In their reference configuration, the scales are oriented parallel to each other with the orientation described in terms of the dihedral angles α 0 and θ 0 ; see Fig.…”

“…Thus, they are now intensely studied as material templates to make armors, smart skins, soft robotics and multifunctional surfaces [10][11][12][13]. Mechanically, scales give rise to fascinating emergent behavior such as strain stiffening, evolving directionality and anomalous frictional response [14][15][16][17][18][19][20][21][22][23][24]. These behaviors can potentially aid organisms in balancing multiple complex and often contradictory functions such as locomotion with protection, and softness with stiffness.…”