Geometry and elasticity of a knitted fabric

TL;DR

This paper investigates the mechanical properties of knitted fabrics, combining experimental measurements with a theoretical model based on yarn bending energy, to better understand their unique elasticity and shape-shifting capabilities.

Contribution

It introduces a first-principles mechanical model for knitted fabrics that accurately predicts their shape and response, advancing fundamental understanding of their elasticity.

Findings

Model agrees quantitatively with experimental data

Knitted fabric elasticity is explained by yarn bending and topological constraints

Provides a framework for designing thread-based smart materials

Abstract

Knitting is not only a mere art and craft hobby but also a thousand year old technology. Unlike weaving, it can produce loose yet extremely stretchable fabrics with almost vanishing rigidity, a desirable property exhibited by hardly any bulk material. It also enables the engineering of arbitrarily shaped two and three-dimensional objects with tunable mechanical response. In contrast with the extensive body of related empirical knowledge and despite a growing industrial interest, the physical ingredients underlying these intriguing mechanical properties remain poorly understood. To make some progress in this direction, we study a model tricot made of a single elastic thread knitted into the common pattern called \textit{stockinette}. On the one hand, we experimentally investigate its tensile response and measure local displacements of the stitches during deformation. On the other hand, we derive a first-principle mechanical model for the displacement field based on the yarn bending energy, the conservation of its total length and the topological constraints on the constitutive stitches. Our model solves both the shape and mechanical response of the knit and agrees quantitatively with our measurements. This study thus provides a fundamental framework for the understanding of knitted fabrics, paving the way to thread-based smart materials.