Kovacs-like memory effect in strain stiffening collagen networks

TL;DR

The paper investigates Kovacs-like memory effects in type-I collagen biopolymer networks, a disordered soft solid, using shear rheology and in-situ boundary imaging. Through a two-step deformation protocol, they observe a non-monotonic stress relaxation with a peak time $t_p$ that scales linearly with waiting time $t_w$, and this memory emerges only in the nonlinear strain-stiffening regime. A strong correlation between memory and negative normal stress is reported, supported by boundary-imaging that reveals spatially distinct, boundary-localized relaxation modes and affine velocity fields during deformation. These findings highlight the role of strain stiffening and normal-stress dynamics in enabling memory formation in biopolymer networks, with implications for designing memory-enabled soft materials and understanding extracellular matrix mechanics.

Abstract

Materials driven far from equilibrium can encode memories of past deformations through long-lived structural reorganisations. Such memory effects-reflecting parameters such as deformation direction, magnitude, and duration have been widely explored in soft amorphous solids. Here, we report a Kovacs-like memory effect manifested as a non-monotonic stress relaxation in vitro biopolymer networks formed by collagen, an essential component of the mammalian extracellular matrix. Using shear rheology combined with in-situ optical imaging, we find that this memory effect emerges exclusively in the nonlinear strain-stiffening regime, and persists over a much broader range of strain amplitudes than previously reported for other viscoelastic amorphous materials. Furthermore, we uncover a strong correlation between the memory response and the development of negative normal stresses and associated strain fields, highlighting the unique nonequilibrium mechanics underlying memory formation in biopolymer networks.

Figures (10)

• Figure 1: (a)Stress-strain curve for 2 mg/ml collagen polymerized at $25^{\circ} C$. The linear relation between stress and strain is marked as the red line. Confocal microscopy image of the network is shown in the inset. (b) Differential shear modulus as a function of shear strain. The differential shear modulus remains constant in the linear response region and increases substantially in the non-linear region. (c) Relaxation curves for different strain values corresponding to the linear and the strain stiffening regions. The shear modulus ($\sigma/\gamma$) is plotted w.r.t. time for various $\gamma$ values. The relaxation rate is higher for applied strains lying in the strain stiffening region compared to the linear region.
• Figure 2: (a) Schematic of the experimental protocol for the Kovacs memory effect. (b) Temporal evolution of stress showing Kovacs effect for $\gamma_1\,=\,40\%, \, \gamma_2 \,=\, 30\%, \, t_w\,=\, 20\,s$, and the inset shows the stress evolution during the second step $\gamma_2 = 30\%$. (c) Relation between the peak position of the stress response during the second step strain perturbation and the waiting time for $\gamma_1 \, = \, 40\%$ for different values of $\Delta \gamma$.
• Figure 3: (a) Time evolution of both shear and normal stresses for a two-step Kovacs memory protocol for $\gamma_1 = 40\%, t_w=20\,s$ and $\gamma_2=35\%$. Both the stresses are normalized with respect to the first point. Normalized shear and normal stresses only for the second step strain deformation are indicated in panel b. Both the peak time $t_p$ in shear stress and dip time $t_d$ in normal stress are close to each other. (c) peak time $t_p$ versus dip time $t_d$ showing good linear correlations, shown as red squares, and the deviations are shown as blue circles. (d) Phase diagram in the parameter plane of $\Delta \gamma$ and $t_w$ for $\gamma_1$ = 40% for correlation between the time evolution of shear and normal stresses. The correlation points are marked as black stars and the anti correlation points are marked as red diamonds.
• Figure 4: (a) Schematic of the in-situ imaging setup. (b) Snapshot of the sample seeded with polystyrene tracer beads at the sample-air interface. (c) Stress-strain curve for 2 mg/ml collagen network seeded with polystyrene tracers polymerized at $25^{\circ}C$. (d) Normalized velocity($v/v_p$) as a function of normalized gap ($x/d$) for different strain values (indicated as the variation in the colorscale).
• Figure 5: (a) Displacement field shown as a vector map indicating inward movement (localized compression of the network) during stress relaxation of the first step strain deformation. The red arrow indicates the moving plate. The distribution of displacement magnitudes (panel b) and the image difference at the sample interface (panel c) during the first step show the prominent sample reorganization near both the static and moving plates. (d) Displacement field shown as a vector map indicating outward movement (localized expansion of the sample) during stress relaxation of the second step strain deformation. The distribution of displacement magnitudes (panel e) and the image difference at the sample interface (panel f) during the second step show the prominent sample reorganization near the moving plate.