arXiv subjects

Lauren Niu

Publications and source records attributed to Lauren Niu.

5 recordsLinked to original sources

arXiv2026

Textiles: from twisted yarn to topology and mechanics

While textiles have existed throughout much of human history as complex mechanical metamaterials, textile science has largely been overlooked by the physics community until recently. In this review, we consider the symmetry, topology, and mechanics of woven and knitted materials, showing that they represent a unique, if under-explored, corner of condensed matter. We start with the basic construction and elementary mechanical model of spun yarn, reviewing recent developments twisted bundle structures. We then introduce woven and knitted fabrics as materials with layer symmetries that can be topologically characterized as knots and links in the thickened torus. We finally discuss fabric mechanics and geometry, invoking recent results surrounding yarn-level and stitch-level geometry, deformations, and defect structures.

cond-mat.soft↗

arXiv2026

Variations on the Three-Sphere: Laves' Labyrinth Lopped

Inspired by the structure of $srs$ Laves networks in $\mathbb{R}^3$ that underpin the celebrated gyroid surface, we construct a Laves network of identical three-coordinated vertices on $S^3$ with double-twist. This network is a subset of the vertices and edges of the 600-cell, and can be viewed as a bipartite graph of disjoint 24-cell vertices inscribed in the 600-cell. We describe mutually entangled realizations of this network on $S^3$, and describe their relation to the well-known $srs$ Laves network structure in $\mathbb{R}^3$.

cond-mat.soft↗

arXiv2024

You Have to Grow Wefts to Fold Them

Knitting turns a one dimensional yarn into a highly ramified three-dimensional structure. As a method of additive manufacturing, it holds promise for a new class of lightweight, ultrastrong materials. Here we present a purely geometric model to predict the three-dimensional folding of knitted fabrics made only of the two traditional stitches, knit and purl.

cond-mat.soft↗

arXiv2022

PullupStructs: Digital Fabrication for Folding Structures via Pull-up Nets

In this paper, we introduce a method to rapidly create 3D geometries by folding 2D sheets via pull-up nets. Given a 3D structure, we unfold its mesh into a planar 2D sheet using heuristic algorithms and populate these with cutlines and throughholes. We develop a web-based simulation tool that translates users' 3D meshes into manufacturable 2D sheets. After laser-cutting the sheet and feeding thread through these throughholes to form a pull-up net, pulling the thread will fold the sheet into the 3D structure using a single degree of freedom. We introduce the fabrication process and build a variety of prototypes demonstrating the method's ability to rapidly create a breadth of geometries suitable for low-fidelity prototyping that are both load-bearing and aesthetic across a range of scales. Future work will expand the breadth of geometries available and evaluate the ability of our prototypes to sustain structural loads.

cs.HC↗

arXiv2021

Geometric mechanics of random kirigami

The presence of cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension. We use numerical experiments to characterize the geometric mechanics of kirigamized sheets as a function of the number, size and orientation of cuts. We show that the geometry of mechanically loaded sheets can be approximated as a composition of simple developable units: flats, cylinders, cones and compressed Elasticae. This geometric construction yields simple scaling laws for the mechanical response of the sheet in both the weak and strongly deformed limit. In the ultimately stretched limit, this further leads to a theorem on the nature and form of geodesics in an arbitrary kirigami pattern, consistent with observations and simulations. By varying the shape and size of the geodesic in a kirigamized sheet, we show that we can control the deployment trajectory of the sheet, and thence its functional properties as a robotic gripper or a soft light window. Overall our study of random kirigami sets the stage for controlling the shape and shielding the stresses in thin sheets using cuts.

cond-mat.soft↗