Ultra-light hierarchical meta-materials on a body-centred cubic lattice

Modern fabrication techniques offer the freedom to design and manufacture structures with complex geometry on many lengthscales, offering many potential advantages. For example, fractal/hierarchical struts have been shown to be exceptionally strong and yet light (Rayneau-Kirkhope D. et al., Phys. Rev. Lett., 109 (2012) 204301). In this letter, we propose a new class of meta-material, constructed from fractal or hierarchical struts linking a specific set of lattice points. We present a mechanical analysis of this meta-material resulting from a body-centred cubic (BCC) lattice. We show that, through the use of hierarchy, the material usage follows an enhanced scaling relation, and both material property and overall efficiency can be optimised for a specific applied stress. Such a design has the potential of providing the next generation of lightweight, buckling-resistant meta-materials

Multi-step self-guided pathways for shape-changing metamaterials

Multi-step pathways, constituted of a sequence of reconfigurations, are central to a wide variety of natural and man-made systems. Such pathways autonomously execute in self-guided processes such as protein folding and self-assembly, but require external control in macroscopic mechanical systems, provided by, e.g., actuators in robotics or manual folding in origami. Here we introduce shape-changing mechanical metamaterials, that exhibit self-guided multi-step pathways in response to global uniform compression. Their design combines strongly nonlinear mechanical elements with a multimodal architecture that allows for a sequence of topological reconfigurations, i.e., modifications of the topology caused by the formation of internal self-contacts. We realized such metamaterials by digital manufacturing, and show that the pathway and final configuration can be controlled by rational design of the nonlinear mechanical elements. We furthermore demonstrate that self-contacts suppress pathway errors. Finally, we demonstrate how hierarchical architectures allow to extend the number of distinct reconfiguration steps. Our work establishes general principles for designing mechanical pathways, opening new avenues for self-folding media, pluripotent materials, and pliable devices in, e.g., stretchable electronics and soft robotics.Comment: 16 pages, 3 main figures, 10 extended data figures. See https://youtu.be/8m1QfkMFL0I for an explanatory vide

Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness

Acknowledgements H.N.G.W. is grateful for support for this work by the ONR (grant number N00014-15-1-2933), managed by D. Shifler, and the DARPA MCMA programme (grant number W91CRB-10-1-005), managed by J. Goldwasser.Peer reviewedPostprintPostprintPostprintPostprin

Thermal Conductivity Of Biomimetic Leaf Composite

The venous morphology of a typical plant leaf affects its mechanical and thermal properties. Such a material could be considered as a fiber reinforced composite structure where the veins and the rest of the leaf are considered as two materials having highly contrast mechanical and thermal properties. The variegated venations found in nature is idealized into three principal fibers—the central mid-fiber corresponding to the mid-rib, straight parallel secondary fibers attached to the mid-fiber representing the secondary veins, and then another set of parallel fibers emanating from the secondary fibers mimicking the tertiary veins of a typical leaf. This paper addresses the in-plane thermal conductivity of such a composite by considering such a venous fiber morphology embedded in a matrix material. We have considered two cases, fibers having either higher or lower conductivity respect to the matrix. The tertiary fibers do not interconnect the secondary fibers in our present study. We carry out finite element based computational investigation of the thermal conductivity of these composites under uniaxial thermal gradients and study the effect of different fiber architectures. To this end, we use two broad types of architectures both having similar central main fiber but differing in either having only secondary fibers or additional tertiary fibers. The fiber and matrix volume fractions are kept constant and a comparative parametric study is carried out by varying the inclination of the secondary fibers. We find the heat conductivity in the direction of the main fiber (Y direction) increases significantly as the fiber angle of the secondary increases. Furthermore, for composite with metal fibers, the conductivity in the Y direction is further enhanced when composite is manufactured by having secondary fibers forming a closed cell structure. However, for composite with ceramic fibers, the conductivity of the composite in the Y direction is little affected by having secondary fibers closed. An opposite behavior is observed when considering conductivity of the composite in the X direction. The conductivity of the composite in the X direction is reduced with increase in the angle of the secondary fibers. Higher conductivity in the X direction is achieved for composite with no closed cells for composites with metal fibers. The results also indicate that for composites with the constant fiber volume fraction, morphology of tertiary fibers may not significantly alter material conductivities. In conclusion, introducing a leaf-mimicking topology in fiber architecture can provide significant additional degrees of tunability in design of these composite structures

Spiderweb Honeycombs

Small and large deformation in-plane elastic response of a new class of hierarchical fractal-like honeycombs inspired by the topology of the “spiderweb” were investigated through analytical modeling, detailed numerical simulations, and mechanical testing. Small deformation elasticity results show that the isotropic in-plane elastic moduli (Young’s modulus and Poisson’s ratio) of the structures are controlled by dimension ratios in the hierarchical pattern of spiderweb, and the response can vary from bending to stretching dominated. In large deformations, spiderweb hierarchy postpones the onset of instability compared to stretching dominated triangular honeycomb (which is indeed a special case of the proposed spiderweb honeycomb), and exhibits hardening behavior due to geometrical nonlinearity. Furthermore, simple geometrical arguments were obtained for large deformation Poisson’s ratio of first order spiderweb honeycombs, which show good agreement with numerical and experimental results. Spiderweb honeycombs exhibit auxetic behavior depending on the non-dimensional geometrical ratio of spiderweb.NPRP award [NPRP 5-1298-2-560] from the Qatar National Research Fund (a member of the Qatar Foundation

Stress analysis in functionally graded rotating disks with non-uniform thickness and variable angular velocity

Stress field in functionally graded (FG) rotating disks with non-uniform thickness and variable angular velocity is studied numerically. The elastic modulus and mass density of the disks are assumed to be varying along the radius as a power-law function of the radial coordinate, while the Poisson's ratio is kept constant. The governing equations for the stress field is derived and numerically solved using the finite difference method for the case of fixed-free boundary conditions. Additionally, the effect of material gradient index (i.e., the level of material gradation) on the stress field is evaluated. Our results show that the optimum stress field is achieved by having a thickness profile in the form of a rational function of the radial coordinate. Moreover, a smaller stress field can be developed by having greater mass density and elastic modulus at the outer radius of the disk (i.e., ceramic-rich composites at the outer radius). The numerical results additionally reveal that deceleration results in shear-stress development within the disks where a greater deceleration leads to greater shear stress; however this has almost no effect on the radial and circumferential stresses. Furthermore, the shear stress can cause a shift in the location of the maximum Von Mises stress, where for small deceleration, maximum Von Mises stress is located somewhere between the inner and outer radii, while for large deceleration it is located at the inner radius.This report was made possible by a NPRP award [NPRP 5–068-2–024] from the Qatar National Research Fund (a member of the Qatar Foundation)