A new concept for superior energy dissipation in hierarchical materials and structures

We consider the elastic energy of a hanging drape -- a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern formation in a thin elastic sheet is of particular interest because the length scale of folding varies with height. We focus on how the minimum elastic energy depends on the physical parameters. As the sheet thickness vanishes, the limiting energ...

A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The results may be used for predictions of the mechanical behavior of materials with multifractal microstructure, as well as for the estimation of the metric, information, and correlation dimensions using experimental data on the elastic behavio...

In many scenarios -- when we bite food or during a crash -- fracture is inevitable. Finding solutions to steer fracture to mitigate its impact or turn it into a purposeful functionality, is therefore crucial. Strategies using composites, changes in chemical composition or crystal orientation, have proven to be very efficient, but the crack path control remains limited and has not been achieved in load-bearing structures. Here, we introduce fracture metamaterials consisting of...

We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in general not well-posed since its solution typically requires the use of infinitesimally fine microstructure. Therefore we examine the effect of singularly perturbing the problem by adding the structure perimeter to the cost. For a uniaxial an...

Fractal structure emerges spontaneously from the chemical cross\-linking of monomers into hydrogels, and has been directly linked to power law visco\-elasticity at the gel transition, as recently demonstrated for isostatic (marginally--rigid) spring networks based on the Sierpinski triangle. Here we generalize the Sierpinski triangle generation rules to produce 4 fractals, all with the same dimension $d_{\rm f}=\log 3/\log 2$, with the Sierpinski triangle being one case. We s...

The design of effective and compact energy absorption systems is key to the survivability and durability of many man-made structures and machines. To this end, this work presents the design, assessment, and implementation of a novel origami-inspired energy absorber that is based on the Kresling origami pattern. The absorber consists of a Kresling origami column positioned between the loading point and an energy dissipation module. By exploiting its unique inherent translation...

Stiff scales adorn the exterior surfaces of fishes, snakes, and many reptiles. They provide protection from external piercing attacks and control over global deformation behavior to aid locomotion, slithering, and swimming across a wide range of environmental condition. In this letter, we investigate the dynamic behavior of biomimetic scale substrates for further understanding the origins of the nonlinearity that involve various aspect of scales interaction, sliding kinematic...

Biomimetic scale-covered substrates are architected meta-structures exhibiting fascinating emergent nonlinearities via the geometry of collective scales contacts. In spite of much progress in understanding their elastic nonlinearity, their dissipative behavior arising from scales sliding is relatively uninvestigated in the dynamic regime. Recently discovered is the phenomena of viscous emergence, where dry Coulomb friction between scales can lead to apparent viscous damping b...

Macroscopic friction coefficients observed in experiments are the result of various types of complex multiscale interactions between sliding surfaces. Therefore, there are several ways to modify them depending on the physical phenomena involved. Recently, it has been demonstrated that surface structure, e.g. artificial patterning, can be used to tune frictional properties. In this paper, we show how the global friction coefficients can also be manipulated using composite surf...

Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly optimized through evolution and natural selection, leading to the biologically and practically relevant problem of understanding and applying the principles of their design. Inspired by the hierarchically organized scaffolding networks found in p...