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

Helical structures are ubiquitous in nature and engineering, ranging from DNA molecules to plant tendrils, from sea snail shells to nanoribbons. While the helical shapes in natural and engineered systems often exhibit nearly uniform radius and pitch, helical shell structures with changing radius and pitch, such as seashells and some plant tendrils, adds to the variety of this family of aesthetic beauty. Here we develop a comprehensive theoretical framework for tunable helical...

In this letter a mathematical model to design nano-bio-inspired hierarchical materials is proposed. An optimization procedure is also presented. Simple formulas describing the dependence of strength, fracture toughness and stiffness on the considered size-scale are derived, taking into account the toughening biomechanisms. Furthermore, regarding nano-grained materials the optimal grain size is deduced: incidentally, it explains and quantitatively predicts the deviation from t...

In this work, a novel hierarchical mechanical metamaterial is proposed that is composed of re-entrant truss-lattice elements. It is shown that this system can deform very differently and can exhibit a versatile extent of the auxetic behaviour depending on a small change in the thickness of its hinges. In addition, depending on which hierarchical level is deforming, the whole structure can exhibit a different type of auxetic behaviour that corresponds to a unique deformation m...

Collagen is a key structural protein in the human body, which undergoes mineralization during the formation of hard tissues. Earlier studies have described the mechanical behavior of bone at different scales highlighting material features across hierarchical structures. Here we present a study that aims to understand the mechanical properties of mineralized collagen fibrils upon tensile/compressive transient loads, investigating how the kinetic energy propagates and it is dis...

Hierarchically structured natural materials possess functionalities unattainable to the same components organized or mixed in simpler ways. For instance, the bones and teeth of mammals are far stronger and more durable than the mineral phases from which they are derived because their constituents are organized hierarchically from the molecular scale to the macroscale. Making similarly functional synthetic hierarchical materials will require an understanding of how to promote ...

The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal dimension. It is shown that the dynamical approach extends the characterization of a curve as a fractal object introducing the effects of mass density, elastic properties, and transverse geometry. The dynamical dimension characterizes mate...

The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles to follow? By introducing the concept of extremal points at different scale levels, a multi-level dissipation element approach has been developed to define structures at different scale levels, in accordance with the concept of structure hi...

We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least amount of material without breaking. Under a simple set of physical approximations and for a certain region of the pressure-brittleness parameter space, we find that a fractal structure in which the plate consists of thicker spars supporting thi...

Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other models of statistical phyics are discussed. We investigate our model on a hierarchical lattice which allows an exact asymptotic renormalization treatment. A surprisingly close analogy is observed between the simulation results on the regular...

Self-similar structures occur naturally and have been employed to engineer exotic physical properties. Here we show that acoustic modes of a fractal-like system of tensioned strings can display increased mechanical quality factors due to the enhancement of dissipation dilution. We describe a realistic resonator design in which the quality factor of the fundamental mode is enhanced by as much as two orders of magnitude compared to a simple string with the same size and tension...