Ultralight, ultrastiff mechanical metamaterials

Abstract

In this study, a new class of materials is reported that show unique material properties such as

an almost constant stiffness per unit mass density. This is contrary to what is commonly

observed in nature where the mechanical properties are poor at low densities. The new class

of materials are made using a manufacturing process known as projection

microstereolithography. This process is combined with a coating technique which is done at

the nanometer scale. The new materials or meta-materials show 3 orders of magnitude

properties higher than ordinary materials.

Introduction

Many materials are found in nature that are highly mechanically efficient. However, as the

density decreases, the mechanical properties also become poorer. For instance, the Youngs

modulus of low-density silica aerogels [1-2] decreases to 10 kPa (0.00001% of bulk) at a

density of less than 10 mg/cm3 (

Specification and fabrication of materials

The materials obtained in this research have an ordered, isotropic structure with a face-

centered cubic architecture. The lattice forming the materials has dimensions ranging from

~20 m down to ~40 nm. The densities of the samples produced in this work ranged from

0.87 kg/m3 to 468 kg/m3, corresponding to 0.025% to 20% relative density. The unit cell is

designed so as to withstand stretching rather than bending. It satisfies the Maxwells criterion

which is given as M = b 3j + 6 > 0. A fundamental lattice building block of this type is the

octet-truss unit cell (Fig. 1A), whose geometric configuration was proposed by Deshpande et

al. [6]. The cell has a regular octahedron as its core, surrounded by eight regular tetrahedra

distributed on its faces.

Fig. 1 Architecture of stretch-dominated and bend-dominated unit cells and lattices.

(A) Mechanical response to compressive loading of a stretch-dominated octet-truss unit cell.

(B) Octet-truss unit cells packed into a cubic microlattice. (C) SEM image of a stretch-

dominated lattice material composed of a network of octet-truss unit cells. (D) Mechanical

response to compressive loading of a bend-dominated tetrakaidecahedron unit cell. (E)

Tetrakaidecahedron unit cell packed into a cubic bend-dominated lattice (Kelvin foam). (F)

SEM image of a bend-dominated lattice composed of a network of tetrakaidecahedron unit

cells.

The samples prepared in this work were analyzed, fabricated, and tested them in a variety of

orientations. In addition, they were fabricated in a range of densities. The fabrication of these

microlattices is enabled by projection microstereolithography, a layer-by-layer additive

micromanufacturing process capable of fabricating arbitrary three-dimensional microscale

structures [7-8]. This type of fabrication technology is ideal for 3D lattices with high

structural complexity and with feature sizes ranging from tens of micrometers to centimeters.

By combining projection microstereolithography with nanoscale coating methods, 3D lattices

with ultralow relative densities below 0.1% were created.

The apparatus in this research uses a spatial light modulatorin this case a liquid-crystal-on-

silicon chipas a dynamically reconfigurable digital photomask. A three-dimensional CAD

model is first sliced into a series of closely spaced horizontal planes. These two-dimensional

image slices are sequentially transmitted to the reflective liquid-crystal-on-silicon chip, which

is illuminated with UV light from a light-emitting diode array. Each image is projected

through a reduction lens onto the surface of the photosensitive resin. The exposed liquid

cures, forming a layer in the shape of the two-dimensional image, and the substrate on which

it rests is lowered, reflowing a thin film of liquid over the cured layer. The image projection

is then repeated, with the next image slice forming the subsequent layer.

Results

The resulting hollow-tube microlattices have alumina thicknesses from ~40 to 210 nm, with

an example shown in Fig. 2, D and H, with corresponding material weight density ranging

from less than 1 kg/m3 to 10.2 kg/m3. The microstructured mechanical metamaterials were

tested to determine their Youngs modulus E and uniaxial compressive strength y, defined as

the crushing stress of the material. Uniaxial compression studies of all microlattices with the

same cubic dimensions were conducted on an MTS Nano Indenter XP, equipped with a flat

punch stainless steel tip with a diameter of 1.52 mm. During 20 consecutive compression

cycles up to 10% strain, typical viscoelastic behavior for the polymer microlattices was

observed with pronounced hysteresis and loading ratedependent Youngs modulus. The

Youngs moduli for all polymer microlattices and foams were extracted at a loading rate at

87.2 nN/s, corresponding to a strain rate of 103

s1

.

When an ultralow-density metallic microlattice is bend-dominated, its stiffness degrades

substantially with reduced density. The metamaterials obtained in this research, in contrast,

maintain their mechanical efficiency over a broad density regime without substantial

degradation in specific stiffness, owing to the nearly linear E- scaling relationship. It was

shown that these high mechanical efficiencies are possible across a range of constituent

materials. Using these findings, new materials can be designed for critical applications in

many fields such as aerospace design for hypersonic transport, spaceships for habitation in

MARS etc.

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