Fibrous gels modelled as fluid-filled continua with double-well energy landscape

Abstract

Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified state over a range of stresses. Continuum chemo-elastic theories can be used to model the mechanical behaviour of these gels, but they suffer from the drawback that the stored energy function of the underlying network is based on neo-Hookean elasticity, which cannot account for the existence of multiple phases. Here we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress–strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite-element calculations. We also perform experiments to show that certain features in the stress–strain curves of fibrous gels predicted by our model can be found in the compression response of blood clots. Our methods may be extended to other tissues and synthetic gels that have a fibrous structure.

Nonlinear Statistical Mechanics Drives Intrinsic Electrostriction and Volumetric Torque in Polymer Networks

“…"frozen in" dipoles) have an electrically-induced compressive stiffness [52]. These cases could give rise to interesting behavior such as microbuckling [53], bistability, and phase transitions when loaded in compression [54,55]. While not relevant to the current study, the implications of these effects on electroactive polymer networks and electromechanical actuation present an interesting opportunity for future research.…”

Mechanics Underpinning Phase Separation of Hydrogels

“…The dependence of χ on other external fields, such as temperature χ = χ­(ϕ), is directly prescribed as variations of χ within a reasonable range from 0 to 2, comparable to that in the literature. , To further show that our method can be easily extended to different χ­(ϕ) functions, in the Supporting Information, we demonstrate the phase behavior of a hydrogel with χ = χ 1 + χ 2 ϕ as an example. It is worth mentioning that there are many other forms of stretching energy considered in the literature, and the stretching energy can also be formulated by choosing the initial fabrication state as the relaxation state of the polymer network, ,− the energy which tends to become double-welled more easily under mechanical constraints. Therefore, here, we show that even with the current stretching energy in (), a hydrogel with a single phase under equilibrium swelling can undergo complex phase behaviors under mechanical constraints.…”

Polymer networks which locally rotate to accommodate stresses, torques, and deformation

“…Biopolymers Many biopolymers such as fibrin and collagen fibers are known to buckle in compression [61,62]; and, as a result, have a nonconvex free energy. Recently, fiber buckling has been proposed as a mechanism for certain densification phase transitions that occur in biopolymer networks resulting in cell remodelling, tethering between cells, and the compression response of blood clots [21,61]. Here we follow recent work [21,61] and assume that the chain free energy is a quartic function of γ.…”

“…Recently, fiber buckling has been proposed as a mechanism for certain densification phase transitions that occur in biopolymer networks resulting in cell remodelling, tethering between cells, and the compression response of blood clots [21,61]. Here we follow recent work [21,61] and assume that the chain free energy is a quartic function of γ. Let γ r = r/r denote the relative chain stretch.…”

“…Here we choose = 0.05. Next, consider the deformation gradient F = diag (λ, 1, 1) where 0 < λ < 1 characterizes the compression of a biopolymer gel [61] with vanishing bulk modulus. FIG.…”