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.

Advanced finite element analysis of L4–L5 implanted spine segment

“…The analyses presented in the paper can be utilised in prosthesis shape design and/or material optimisation. Also they may be further extended for damage and poromechanical effects [38,39]. The limitation of the constitutive model presented in the paper is that it was formulated on the basis of relaxation tests and monotonic compression tests.…”

Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients

“…that is the external force due to the weight where we have used the following intermediate results, In the following, we calculate the edge forces that are necessary to have the displacement field (45). Such forces per unit line are also graphically represented in the second row of Fig.…”

“…The kinematical restrictions (44) imply no displacement at vertices V 1 and V 2 and no horizontal displacement at vertices V 3 and V 4 . This means that the external (or reaction) wedge forces in order to keep the displacement field in (45) are from (41), (42) and (43), f ext α = −P 2α1 − P 1α2 for wedges V 1 and V 3 and the opposite f ext α = P 2α1 + P 1α2 for wedges V 2 and V 4 . We have from (42), (45) and (47) …”

“…This means that the external (or reaction) wedge forces in order to keep the displacement field in (45) are from (41), (42) and (43), f ext α = −P 2α1 − P 1α2 for wedges V 1 and V 3 and the opposite f ext α = P 2α1 + P 1α2 for wedges V 2 and V 4 . We have from (42), (45) and (47) …”

“…Another possibility is to consider higher-order gradient theories, in which the deformation energy depends on second and/or higher gradients of the displacement [17,33,40]. This is done in the literature for both monophasic systems (see [14,15,19,22,24,25,44,57], in which continuous systems are investigated, and [1,26,56,64] for cases of lattice/woven structures) and for biphasic (see, e.g., [16,18,20,21,41,45,60,61]) or granular materials [72]. Unlike classical Cauchy continua [4,62,63], second-and higher-order continua can respond to concentrated forces and other generalized contact actions (highly localized stress/strain concentration effects are studied, e.g., in [10]).…”