Micro-poromechanics model of fluid-saturated chemically active fibrous media

Abstract

We have developed a micromechanics based model for chemically active saturated fibrous media that incorporates fiber network microstructure, chemical potential driven fluid flow, and micro-poromechanics. The stress-strain relationship of the dry fibrous media is first obtained by considering the fiber behavior. The constitutive relationships applicable to saturated media are then derived in the poromechanics framework using Hill's volume averaging. The advantage of this approach is that the resultant continuum model accounts for the discrete nature of the individual fibers while retaining a form suitable for porous materials. As a result, the model is able to predict the influence of micro-scale phenomena, such as the fiber pre-strain caused by osmotic effects and evolution of fiber network structure with loading, on the overall behavior and in particular, on the poromechanics parameters. Additionally, the model can describe fluid-flow related rate-dependent behavior under confined and unconfined conditions and varying chemical environments. The significance of the approach is demonstrated by simulating unconfined drained monotonic uniaxial compression under different surrounding fluid bath molarity, and fluid-flow related creep and relaxation at different loading-levels and different surrounding fluid bath molarity. The model predictions conform to the experimental observations for saturated soft fibrous materials. The method can potentially be extended to other porous materials such as bone, clays, foams and concrete.

Keywords: Poromechanics; creep; drained stress-strain behavior; fiber; micromechanics; osmotic pressure.

Fig. 1

(a) Schematic of dry fibrous network at the microscale. (b) Schematic of saturated fibrous network at microscale by zooming in to a homogenized representative volume element at the macroscale.

Fig. 2

Unconfined uniaxial drained monotonic compression: stress-strain behavior under varying external bath molarity (a, b and d), evolution of pore pressure (c), volume change (e), porosity (f), material properties (g–l), and the fiber stress distributions (m).

Fig. 3

Creep response under different axial stress: strain (a, and b), pore pressures (c–e), volume change (f), material properties (g–l), and the fiber stress distributions (m).

Fig. 4

Creep response under different external bath molarities: strain (a, and b), pore pressures (c–e), volume change (f), material properties (g–l), and the fiber stress distributions (m).

Fig. 5

Comparison of creep response under confined and unconfined conditions for same applied stress and external bath molarity: strain and effective stress (a, b and d), pore pressures (c and e), porosity (f), volume change (g), material properties (h–l), and the fiber stress distributions (m).

Fig. 6

Unconfined stress relaxation under different external bath molarities: axia stress (a), lateral strain (b), pore pressures (c–e), volume change (f), material properties (g–l), and the fiber stress distributions (m).

Fig. 7

Comparison with experimental data: (a) Calibration of osmotic pressure measurements [72], (b) Monotonic stress-strain behavior of articular cartilage under compression [66], (c) apparent Poissons ratio of articular cartilage under monotonic compression [66]. (d) Experimental data for creep of articular cartilage [69], and e) Model prediction for creep of articular cartilage.