Engineering the shape and structure of materials by fractal cut

Abstract

In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.he physical properties of materials are largely determined by structure: atomic/molecular structure, phase distribution, internal defects, nano/microstructure, sample geometry, and electronic structure. Among these, engineering the geometry of the sample can provide a direct, intuitive, and often materialindependent approach to achieve a predetermined set of properties. Metamaterials are fabricated based on geometric concepts (1-16). In two dimensions, periodic geometries have been adopted to tune the mechanical properties of membranes (3-8, 10, 12-14). From simple shapes such as circles (3), triangles (6,7,12,13), and quadralaterals (4, 5, 14) to more complex shapes (8, 10), a broad range of mechanical behavior has been observed, including pattern transformation, negative Poisson's ratio (auxetic), elastic response, and isostaticity. Origami and kirigami, the arts of paper folding and paper cutting, create beautiful patterns and shapes that have attracted the attention of scientists to two-dimensional materials (e.g., graphene, polymer films, and so on) (11,(17)(18)(19). However, application of conventional origami and kirigami approaches to achieve desired material response requires complex cutting and/or folding patterns that are often incompatible with engineering materials. In this paper we propose an advanced approach to the design of two-dimensional structures that can achieve a wide range of desirable programmed shapes and mechanical properties.This study starts from the question, Can we design twodimensional structures that can be formed by simply cutting a sheet, that can morph into a specific shape? In nature, many biological and natural system (20) can be found that use hierarchical structure to produce different properties and/or shapes. One such example is a stem cell. An embryonic, pluripotent stem cell can differentiate into any type of cell in the body (21). By recursively dividing, the stem cell can transform into particular cell types or remain unspecialized with the potential to transform. For a material, one aspect of recursive hierarchical geometry was recently discussed for applications in flexible electronics (22). Here, by analogy to the stem cell, we demonstrate that starting from a simpl...

Fracture of graphene: a review

“…27 a Controlled cut of graphene with nickel nanoparticles (Ci et al 2008): SEM image of the nanocut channels on a graphite surface (top) and formation of a zigzag edged channel simulated by Monte Carlo methods. b Fractal cut of a Korean traditional hat and hairstyle realized by engineering the distribution of hierarchy and motif (Cho et al 2014): a Tangon hat (top), a Gache hairstyle (middle), and a Jeongjaguan hat (bottom) pression fracture of graphene follows Griffith's criterion with an energy release rate around 10 J/m 2 , very close to that under tensile fracture. The cut induced by ejection of atoms is often closed by bond reconstruction across the sites of the missing atoms, causing a local kink along the length of the nanotube.…”

Lattice Metamaterials with Mechanically Tunable Poisson’s Ratio for Vibration Control

“…Between the various architectures it is worth to note dimpled and perforated elastic sheets [47], origami/Kirigami-based metamaterials [18,48,49], hierarchical metamaterials with fractal cuts [50] and foams [51][52][53][54][55]. Auxetic materials and structures are intrinsically multifunctional because of the coupling originated between their unusual deformation mechanisms and their multiphysics behavior.…”

Patterning via self-organization and self-folding: Beyond conventional lithography

“…24 Self-folding has been used in various applications, including self-folding robots ( Figure 3 a-b ), 25 microgrippers ( Figure 3d-f ), 26 solar cells, 27 and origami antennas. 28 The use of strategic cuts in materials followed by folding (kirigami) enables, for example, the formation of stretchable electrodes for nonplanar devices ( Figure 3c ) 29 and solar cells with integrated solar tracking. 30 Structures formed by self-folding and self-organization can be classifi ed based on their characteristic length scales, range of materials, and form factors, as summarized in Table I .…”