Geometry of Materials


Our group studies the effects of microstructural geometry on the physical properties in a wide variety of soft materials.

What a Tangled Web We Weave

Fabrics oriented perpendicular to the ground (top) and those rotated by 45° (bottom) have very different draping behavior.

Spinning and weaving were some of the first technologies developed by man. These historical inventions continue to influence daily life, yet only at an empirical level do we understand the remarkable physical and material properties they can achieve. Spinning simply adds twist to fibers, vastly increasing tensile strength while maintaining flexibility. Weaving and knitting use single threads to generate durable yet pliant two-dimensional surfaces. Woven fabrics, inextensible along the warp and weft directions, have a soft shear direction whih varies with the weave. While with a greater intrinsic elasticity, knits have two independent elastic moduli and a complex, out-of-plane bending response. Ultimately, the inherent anisotropy of both woven and knitted fabrics unites their descriptions. Building upon microscopic properties of the thread, from twist to chemistry to friction, my group will seek a set of local rules that control the global behavior of fabrics. Such a constitutive model will develop an understanding of the full range of fabric deformations, crucial for such applications as mechanoresponsive garments to biocompatible weaves and networks used in tissue engineering. Beyond technological advances, such a model will shed light on fundamental questions, such as polymer entanglement or the mechanical properties of biological tissue and networks.

Shown above: swatches of stockinette stitch fabric knitted on the lab's replica Taitexma Industrial knitting machine.

Historic Mechanical Metamaterials

A series of pleats and knots – known as smocking – gives an inextensible woven fabric emergent elastic properties.

One might be surprised to learn that the first mechanical metamaterial was invented during the middle ages. The medieval embroidery known as smocking uses knots to constrain a regular set of pleats, thereby converting local bending energy into bulk stretching energy. Modern smocking techniques sacrifice maximal extension to give the material biaxial stretch. This quickly becomes a complex mathematical question coming from the strict constraints of rigid origami imposed by the inextensibility of paper. Relaxing these constraints using woven fabrics opens up a zoo of possible configurations. Working with model and experimental systems, my group will design and create materials, such as mechanical metamaterials and auxetics, with emergent properties due to imposed microstructure.

Programmable Matter

A mathematical model for geometric shape change can design a series of elastic anisotropies required for a material to transform into a target shape.

The nascent technique of 4D printing has the potential to revolutionize manufacturing in fields ranging from organs-on-a-chip to architecture to soft robotics. By expanding the pallet of 3D printable materials to include the use stimuli responsive inks, 4D printing promises precise control over patterned shape transformations. Our collaboration with the Lewis Lab turned a unique material and printing method – which enable the direct writing of local anisotropy into both the elastic moduli and the swelling response of the ink – into a predictive manufacturing technique for arbitrarily complex, morphable structures. By implementing a fully anisotropic model of thin film mechanics, not only can we predict the final transformed geometry from a given design, but my model generates the specific pattern of anisotropies needed to produce a target structure.

Emergent Chirality: or The Undeniable Pervasiveness of Twisting

Chiral superstructure formed from achiral particles and achiral interactions. (Image curtesy of A Dastan.)

Molecular chirality acts as a source of frustration in self-assembled, layered systems, such as smectic liquid crystals. In some situations, however, this frustration seeds the emergence of interactions at a wide range of length scales, which lead to the development of complex, hierarchical structures. Understanding the microscopic interactions responsible for such intricate architectures is of paramount importance to being able do design self-assembled systems of arbitrary complexity. Such chiral assemblies also form from achiral constituents, such as block copolymers, amphiphiles and lipids. Assembly of a simple system – oblate ellipsoids in a solvent of spheres – sheds light on the emergence of chirality as a packing problem in the presence of steric constraints. Additionally, such notions serve as building blocks to design the guided self-assembly of braids and weavings from filaments decorated with specific binding sites.


Knitting in the news

Presentations at the 2019 APS March Meeting in Boston, MA led to media interest in our knitting work and the following articles:

Interested in non-euclidean spaces? Try them here!

Ever wondered what it would be like to walk around in curved space? Well now you can! Andrea Hawksley, Vi Hart, Sabetta Matsumoto and Henry Segerman have just launched H³ and H²×E as VR simulators of three-dimensional hyperbolic space and two-dimensional hyperbolic space cross the euclidean line.