Unifying model for the rheological behavior of hygroresponsive materials

Hygroresponsive materials exhibit a complex structure-to-property relationship. The interactions of water within these materials under varying hygric and mechanical loads play a crucial role in their macroscopic deformation and final application. While multiple models are available in literature, many lack a comprehensive physical understanding of these phenomena. In this paper, we introduce a stick-slip fiber bundle model that captures the fundamental behaviors of hygroresponsive materials. We incorporate moisture-dependent elements and rules governing the initiation and relaxation of slip strains as well as failure to the statistical approach offered by fiber bundle models. The additional features are based on well-founded interpretations of the structure-to-property relationship in cellulosic materials. Slip strains are triggered by changes in load and moisture, as well as by creep deformations. When subjected to moisture cycles, the model accumulates slip strains, resulting in mechanosorptive behavior. When the load is removed, slip strains are partially relaxed, and subsequent moisture cycles trigger further relaxation, as expected from observations with mechanosorptive material. Importantly, these slip strains are not considered plastic strains; instead, they are unified, nonlinear frozen strains, activated by various stimuli. Failure of fibers is defined by a critical number of slip events allowing for an integrated simulation from intact, via damaged, failed states. We investigate the transition between these regimes upon changes in the hygric and mechanical loading history for relevant parameter ranges. Our enhanced stick-slip fiber bundle model increases the understanding of the intricate behavior of hygroresponsive materials and contributes to a more robust framework for analyzing and interpreting their properties.

Figure 1

Main features observed in hygroresponsive materials. The strain ($\varepsilon$) is presented in black, while the load ($\sigma$) and relative humidity (RH) are represented by red, respectively, blue dashed lines. Letters indicate different features like H for hygroexpansion, E for elasticity, VE for viscoelasticity, and MS for mechanosorption.

Figure 2

Micromechanical interpretation of stick-slip dynamics on wood fibers. We present a wood fiber on the left with its microfibril aggregates exposed. Following to the right, the aggregates' interactions and their behavior under mechanical and moisture stimuli are presented. ${\varepsilon }_d$ and ${\varepsilon }_w$ are the nonslip strain at the dry state and wet state, respectively, while ${\varepsilon }_d^S, {\varepsilon }_w^S$, and ${\varepsilon }_t^S$ are the slip strains respective to drying, wetting, and time evolution.

Figure 3

Sketch of the FBM with green representing slip, yellow tensile, and red compressive strains. On the right is the rheological representation of a single fiber model with elastic, viscoelastic, hygro-expansive, and slip element in series. The total strain $\varepsilon$ is present in both representations.

Figure 4

Flowchart of implemented code.

Figure 5

SS-FBM normalized strain over the normalized time. Solid lines represent the normalized strain $\varepsilon /{\varepsilon }_c$, while dashed lines represent the normalized strain without slip $(\varepsilon -\langle {\varepsilon }^S\rangle )/{\varepsilon }_c$. Line colors resemble softening ratios $D_w/D_d$.

Figure 6

Residual normalized stresses (a) and number of slip events (b) for each fiber of the bundle at $t=40\tau$ in Fig. 5.

Figure 7

SS-FBM strain over five moisture cycles. Solid lines represent total values of $\varepsilon$ and ${\varepsilon }^S$ in both plots, respectively, while dashed lines represent their labeled components.

Figure 8

SS-FBM slip strain evolution over ten moisture cycles and the respective normalized slip (green) and reverse slip (black) avalanches.

Figure 9

Probability density of slip thresholds for increasing moisture cycles MC with identical legend.

Figure 10

SS-FBM maximum strain-stress relation for different dry-to-wet compliance ratios and comparison to the strength with the dry FBM (inset).

Figure 11

Applied load over the number of cycles that can be imposed before the failure of the system. If the system doesn't fail, the maximum number of imposed cycles is 50.

Figure 12

Comparison of the proposed model (SS-FBM) results to empirical data and the hygrolock modeling approach proposed by Dubois et al. [42].