Plasticity, hysteresis, and recovery mechanisms in spider silk fibers

TL;DR

Spider silk exhibits pronounced plasticity, hysteresis, and recovery under cyclic loading, and the microstructural origins have been unclear. The authors develop a microscopically motivated energy-based framework that decouples the fiber response into two parallel networks: an elasto-plastic bond network governing initial stiffness and yield, and an elastic entropic chain network enabling large deformations, with state variables such as $λ_{ul}^{(p)}$, $λ^{(r)}$, and $λ^{(l)}$ tracking the cycle. The model captures hysteresis and residual strain during unloading and shows recovery via bond reformation and chain reorganization that locks a new, stiffer equilibrium, increasing $E$ and $σ_y$ in subsequent cycles, with quantitative agreement to Argiope bruennichi dragline silk data. This work links microstructural evolution to macroscopic cyclic response and provides a predictive framework for engineering bio-inspired fibers with tunable stiffness, yield, energy dissipation, and recovery.

Abstract

Spider silk is a remarkable biomaterial with exceptional stiffness, strength, and toughness stemming from a unique microstructure. While recent studies show that silk fibers exhibit plasticity, hysteresis, and recovery under cyclic loading, the underlying microstructural mechanisms are not yet fully understood. In this work, we propose a mechanism explaining the loading-unloading-relaxation response through microstructural evolution: initial loading distorts intermolecular bonds, resulting in a linear elastic regime. Upon reaching the yield stress, these bonds dissociate and the external load is transferred to the polypeptide chains, which deform entropically to allow large deformations. Unloading is driven by entropic shortening until a traction free state with residual stretch is achieved. Subsequently, the fiber recovers as chains reorganize and bonds reform, locking the microstructure into a new stable equilibrium that increases stiffness in subsequent cycles. Following these mechanisms, we develop a microscopically motivated, energy-based model that captures the macroscopic response of silk fibers under cyclic loading. The response is decoupled into two parallel networks: (1) an elasto-plastic network of inter- and intramolecular bonds governing the initial stiffness and yield stress, and (2) an elastic network of entropic chains that enable large deformations. The model is validated against experimental data from Argiope bruennichi dragline silk. The findings from this work are three-fold: (1) explaining the mechanisms that govern hysteresis and recovery and linking them to microstructural evolution; (2) quantifying the recovery process of the fiber, which restores and enhances mechanical properties; and (3) establishing a predictive foundation for engineering synthetic fibers with customized properties.

Figures (5)

• Figure 1: Microstructural evolution of the spider silk network during a uniaxial cyclic loading test: (a) the initial referential fiber, (b) the loaded state, deformation governed by the dissociation of intermolecular bonds and entropic chain stretching, (c) the unloaded traction free state with a residual stretch $\lambda_{ul}^{(p)}$ due to a decrease in intermolecular bond-density, (d) the relaxed traction free state in which the intermolecular bonds reform to fix the chains and lock the fiber in an elongated configuration with a stretch $\lambda^{(r)}$, and (e) the reloading of the fiber, which is characterized by a stiffening due to the reformation of the bonds and the higher chain stretches.
• Figure 2: Schematic decomposition of the macroscopic mechanical response of spider silk fibers into two networks connected in parallel: (left) a network that captures the elasto-plastic mechanisms, governed by the dissociation of intermolecular and intramolecular bonds, and (center) a network of entropic chains that stretch elastically. (Right) The two springs connected in parallel. The bottom of the figure plots the stress-stretch curves corresponding to the elasto-plastic network (red), the entropic network (blue), and the macroscopic stress-strain curve (black), which is the summation of the two contributions.
• Figure 3: (a) The unloading and (b) the relaxation mechanisms governing the recovery of the spider silk fiber. The unloading phase is characterized by entropic chain shortening and coiling, leading to a residual stretch. The relaxation phase in the traction free state involves the reorganization of the chains in the network and the reformation of intermolecular bonds, which fix the microstructure and lead to a stiffening in the subsequent loading cycle.
• Figure 4: Loading of a spider silk fiber: (a) true stress $\sigma$ as a function of the stretch $\lambda$. The continuous curve corresponds to the model predictions and the circle marks denote the experimental findings of Jiang2023. (b) The stress due to the distortion of the intermolecular bonds $\sigma^{\left(b\right)}$ (Eq. \ref{['eq:stress_elasto-plastic']}), the entropic stress $\sigma^{\left(n\right)}$ (Eq. \ref{['eq:uniaxial_stress_chain_network']}), and the total stress $\sigma=\sigma^{\left(b\right)}+\sigma^{\left(n\right)}$ (Eq. \ref{['eq:stress']}) as a function of the stretch $\lambda$.
• Figure 5: Cyclic loading of a spider silk fiber: true stress $\sigma$ as a function of the stretch $\lambda$ for (a) cycles 2 and 3 and (b) cycles 20 and 30 in the work of Jiang2023. The continuous curve corresponds to the model predictions and the circle marks denote the experimental findings of Jiang2023.