Supercontraction-Induced Twist in Spider Silk Is a Dual Poynting Effect

TL;DR

The paper addresses humidity-driven torsion in spider dragline silk and shows that a dual Poynting effect can arise from nonlinear anisotropic elasticity without invoking intrinsic helicity. It introduces a minimal, microstructure-informed fiber-reinforced cylinder model in which an axially prestretched crystalline phase (β-sheet nanodomains) couples to a hydrated amorphous matrix whose shortening drives remodeling; the constitutive law uses a transversely isotropic energy density $W(I_1,I_4,I_5)$ and kinematics governed by $F$ and the invariants. A diffusion-based hydration model with an irreversible remodeling rule $\\dot c=\beta(RH(t)-c)$ links humidity history to internal strains, enabling quantitative reproduction of monotonic and cyclic torsion in experiments with parameter values consistent with silk physiology. The results establish humidity-induced torsion as a generic outcome of internal remodeling in matrix–fiber composites and provide a compact framework for designing humidity-responsive torsional actuators in soft materials.

Abstract

Spider dragline silk supercontracts as humidity increases, displaying large axial shortening together with a reproducible macroscopic twist. The physical origin of this torsion remains debated and is often attributed to helically arranged load-bearing elements, despite the lack of direct evidence for helicity in the native fiber. Here we show that torsion can arise generically from nonlinear anisotropic elasticity: humidity-driven shortening of the amorphous matrix, mechanically constrained by stiff, axially aligned $β$-sheet--rich load-bearing segments and their experimentally induced prestretch, drives the system into a dual Poynting regime in which axial shortening couples to spontaneous twist. Coupling a diffusion-based water-uptake law to irreversible matrix remodeling and fiber plasticity, the model quantitatively reproduces monotonic and cyclic torsional measurements using parameter values consistent with available experimental material parameters. These results identify supercontraction-induced torsion in spider silk as a manifestation of a dual Poynting effect and provide a minimal, physically grounded framework for humidity-driven torsional actuation in matrix--fiber architectures.

Figures (4)

• Figure 1: Scheme of spider silk structure and wetting supercontraction effect. In the middle scheme we show the classical purely extensional assumption and in the third one we show the experimentally observed combined extensional-torsional supercontraction behavior
• Figure 2: Microstructure-inspired schematic of the constitutive assumptions. (a) In the dry reference state, aligned stiff protein chains associated with hydrophobic $\beta$-sheet nanocrystals act as reinforcing fibers embedded in an isotropic soft amorphous matrix. (b) Under an external axial load, these reinforcing fibers undergo plastic deformation, resulting in a residual prestretch. (c) Upon hydration, water molecules disrupt hydrogen bonds in hydrophilic secondary structures (coils, $\beta$-turns, helices) within the amorphous matrix, enabling entropic recoiling of the chains and an effective shortening of the matrix. (d) In the supercontracted state, this matrix shortening, transmitted through matrix--fiber coupling to the prestretched crystalline fraction, gives rise to both macroscopic axial shortening and torsional deformation of the silk fiber.
• Figure 3: Versicolor dragline silk fibers ($R_e=3.35\,\mu$m, $H=88$ mm expexp): experiments (markers) versus model predictions (solid lines) for (a) monotonic and (b) cyclic humidity protocols. Model parameters: $\mu_T=50$ MPa, $E_L=200$ GPa, $\mu_L=1$ MPa, $\alpha=0.12$, $D=1.6\times10^{-14}$ m$^2$/s, $\lambda_f^{\rm res}=1.1$ (a);sm $\mu_T=82$ MPa, $E_L=250$ GPa, $\mu_L=1$ MPa, $\alpha=0.56$, $D=1\times10^{-14}$ m$^2$/s, $\lambda_f^{\rm res}=1.1$ (b). See End Matter for details.
• Figure 4: Versicolor dragline silk fibers ($R_e=3.35\,\mu$m, $H=88$ mm expexp): experimental RH (markers) and model predictions (solid lines) for the internal normalized water concentration $c$ (dark blue) and fraction of intact hydrogen bonds $m$ for (a) monotonic and (b) cyclic humidity protocols. Model parameters: $\mu_T=50$ MPa, $E_L=200$ GPa, $\mu_L=1$ MPa, $\alpha=0.12$, $D=1.6\times10^{-14}$ m$^2$/s, $\lambda_f^{\rm res}=1.1$ (a); $\mu_T=82$ MPa, $E_L=250$ GPa, $\mu_L=1$ MPa, $\alpha=0.56$, $D=1\times10^{-14}$ m$^2$/s, $\lambda_f^{\rm res}=1.1$ (b).