Return point memory in knitted fabrics

TL;DR

This work reveals that knitted fabrics exhibit robust return point memory under uniaxial cyclic loading, where the stress response remembers the maximum prior strain $\varepsilon_{\mathrm{max}}$ and forms nested, congruent hysteresis loops that wipe out when a higher maximum is reached. The authors develop an extended Preisach model in which yarn-contact hysterons are modulated by an entanglement strain $\varepsilon_t$ and $\varepsilon_{\mathrm{max}}$, decomposing $\varepsilon = \varepsilon_e + \varepsilon_t$ with $\sigma = E(\varepsilon_{\mathrm{max}})\,\varepsilon_e$, and enforcing evolution via a rebound inequality and KKT conditions. The model reproduces nonlocal memory, wiping-out, and congruency observed in experiments and provides a simple, tunable framework for memory in loop-based fabrics. These findings have implications for designing memory-enabled textiles for soft robotics, sensors, and morphing devices, and motivate exploration of memory across diverse fabric architectures by controlling topology, tension, and material composition.

Abstract

The tunable mechanical response of knitted fabrics underpins applications ranging from soft robotics and artificial muscles to morphing electromagnetic field sensors. Elasticity in fabrics emerges from the bending of yarn in the knitted structure; however, properties beyond elasticity are relatively unexplored. Here, we demonstrate that knitted fabrics subjected to cyclic uniaxial stress exhibit significant hysteresis and the remarkable ability to "remember" their response to previous deformations -- reminiscent of classical return point memory in magnetic systems. The hysteretic behavior deviates from the two standard models of hysteresis that usually apply to solid-state materials, viscoelasticity and plasticity. Thus, we develop a phenomenological extension of the Preisach model of hysteresis which well replicates our data, and discuss implications of these results on the underlying mechanisms of memory in knitted fabrics.

Figures (4)

• Figure 1: a) A ribbed fabric machine-knitted from acrylic fingering-weight yarn, stretched horizontally to show the full structure. The horizontal direction is the course and vertical is the wale. b) Zoomed-in fabric to show two unit cells, overlaid with a schematic of the yarns. Entangled regions are identified with blue arrows. Overlay provided by Michael Dimitriyev (private communication, October 2023) c) Experimental setup. The fabric is attached to custom made clamps with paperclips. The length of the fabric in the zero strain state, defined in App. \ref{['sec:dstar']}, is $131\,\textrm{mm}$. The bottom clamp is connected to the base and the top clamp to the crosshead of an Instron universal testing machine, with which we take the sample through repeated load (crosshead moves up)--unload (crosshead moves down) cycles. More information about the sample fabrication and setup are detailed in App. \ref{['sec:fabrication']} and App. \ref{['sec:instrumentation']}. d) First loading (red solid line), first unloading (red dashed line), together with second loading curves (orange solid line) show significant hysteresis in the fabric response.
• Figure 2: a) Idealized return point memory for a fabric first cycled to a given strain $\varepsilon_1$ then subsequently to twice that strain, i.e., $\varepsilon_2$. The first cycle to the lower strain $\varepsilon_1 \sim 7.5\%$ is shown in red. The return point, $\sigma_1(\varepsilon_1)$, is denoted by $A$. Subsequent strain cycles to $\varepsilon_1$ follow the path $0 \longrightarrow A \longrightarrow 0$. The first cycle to higher strain $\varepsilon_2 \sim 15\%$ is shown in green and reaches a new return point $B$. Subsequent cycles to $\varepsilon_2$ follow the blue loading curve $0\longrightarrow C \longrightarrow B$ and the green unloading curve. When the fabric is subsequently cycled to $\varepsilon_1$ again, the loading reaches return point $C$. b) Experimental data for these strain cycles, first cycle in red, second in orange, and henceforth. c) When the fabric is first cycled from zero strain to $\varepsilon_\textrm{max}$ (red then orange curves), subsequent cycles to intermediate strains form nested loops, which rejoin the larger loop only at the extrema, within the larger loop (teal and blue curves). d) Measured nested hysteresis curves, including the reconnection paths between nested loops. The measurements were performed at $\dot{\Delta} = 0.25$ mm/s for a fabric of initial length $L = 131$ mm.
• Figure 3: Measurements of cycles between zero strain (systematically defined in App. \ref{['sec:dstar']}) and $\varepsilon_1\approx 0.075$ followed by cycles to $\varepsilon_2\approx 0.15$ done at three different strain rates corresponding to a)$\dot\Delta = 0.025\textrm{mm/s}$, b)$\dot\Delta = 0.25\textrm{mm/s}$ and c)$\dot\Delta = 2.5\textrm{mm/s}$. The fabric's initial length was $L = 135$ mm. Between each measurement, the fabric was taken off the universal testing machine and rested horizontally on a table for ten minutes. These measurements were done on the same sample, which was identically prepared to the sample measured in Figs. \ref{['fig:experiments']} and \ref{['fig:RPM']}.
• Figure 4: a) Numerical simulation of a tensile test of a knitted fabric utilizing an extended Preisach model reproduces the experimental results very well. b) Taking into account the nested looping confirms that the three key features - non-local memory, wiping-out and congruency - are captured in the model. Note the initial stress of the simulation is set a priori to the initial stress from the experiments.