Multi-level mechanical modeling and computational design framework for weft knitted fabrics

TL;DR

The paper tackles the challenge of predicting and optimizing the mechanical behavior of weft knitted fabrics across material and pattern variations. It develops a multi-scale workflow that starts with a volumetric FE of a representative stitch unit to capture yarn-scale mechanics, then distills this into a three-parameter strain-energy surrogate based on an in-plane anisotropic formulation, and finally extends to heterogeneous knits via simple series/parallel analogies. The approach is validated against biaxial and uniaxial tests, achieving typically less than 5% normalised error, and demonstrated through the design of a uniform-stress tubular compression sleeve. This framework enables rapid, accurate design exploration for next-generation functional knits and could accelerate development in wearables and soft robotics.

Abstract

This work presents a multi-level modeling and design framework for weft knitted fabrics, beginning with a volumetric finite element analysis capturing their mechanical behavior from fundamental principles. Incorporating yarn-level data, it accurately predicts stress-strain responses, reducing the need for extensive physical testing. A simplified strain energy approach homogenizes the results into three key variables, enabling rapid, accurate predictions in minutes. After validation against experiments, our framework can simulate new knit fabrics without additional tests. In real-world scenarios, fabrics often feature variations in yarn materials or patterns. The framework extends to heterogeneous fabrics, showing that transitions between distinct regions can be captured using simple mechanical analogies: springs in series and parallel. This allows heterogeneous textiles to be treated as idealized patchworks of homogeneous pieces, preserving predictive accuracy. The method is demonstrated by designing and producing a compression sleeve with uniform pressure, illustrating how the framework supports development of knits tailored to specific assistance levels and anatomical features. By combining volumetric finite element analysis, simplified model through homogenization, and controlled material transitions, this approach provides a scalable, high-fidelity path toward next-generation weft knitted fabric design.

Figures (7)

• Figure 1: Principles of knitted fabrics. (Left) Knits are made of a hierarchical microstructure, starting from bundles of fibers; their response can be modulated using three variables: material of the fibers, pattern, and stitch-length. (Right) By geometrically reconstructing the knit patterns, we use the material properties of the yarns to build a volumetric finite-element analysis of a representative knit unit of 2 x 2 knots; this behavior can be generalized to simulate homogeneous knit samples and eventually to optimize the stress and strain in a garment - a compressive sleeve with even pressure distribution.
• Figure 2: Yarn testing methodology; microscopy images of nylon A. yarn and B. knit fabric sample; illustration of test procedure and results for cotton yarn testing in C. tension and D. compression; the confidence area represents $\pm$ one standard deviation from the mean, computed from $n=3$ samples.
• Figure 3: Fabric swatch numerical modeling and experimental methodology; A. Finite Element (FE) model showing the geometry of a 2$\times$2 knit stitches (2 stitches in the course and the wale direction); parameters for the centerline, and color-coded boundaries that are tied to enforce periodicity; B. Biaxial experimental stage for biaxial testing of the cruciform fabric swatches; global stress is measured using load cells and local strain is measured using four markers and digital image correlation; C. Normalized Force-Displacement plot of a benchmark knit sample in both X (course) and Y (wale) directions from the FE simulation, reduced-order model, and experiment ($n=3$). Qualitative comparisons between FE and experiments are shown inset at different normalized displacements. In the FE, the color represents the maximum absolute principal stress, ranging from 6 MPa in tension to –4 MPa in compression, where white indicates no stress. D. Effect of the fitting parameters a, b, and $\theta$ on the stress-stretch response.
• Figure 4: Varying microstructure and mechanical response of three types of knit variation in the course direction: A. stitch length, B. pattern, and C. yarn material; the benchmark SL11, Jersey, Cotton is represented twice with a yellow outline; the normalized force-displacement curves show the experimental, simulated, and fitted responses for three variations in each category; the confidence area represents $\pm$ one standard deviation from the mean, calculated from $n=3$ samples.
• Figure 5: Fitting parameters $a$, $b$ and $\theta$ of the strain energy model for three types of variations. The red line at $\theta = 45^\circ$ indicates identical stress in course and wale directions under equibiaxial loading.