The consolidation behavior of silk hydrogels.

Hydrogels have mechanical properties and structural features that are similar to load-bearing soft tissues including intervertebral disc and articular cartilage, and can be implanted for tissue restoration or for local release of therapeutic factors. To help predict their performance, mechanical characterization and mathematical modeling are the available methods for use in tissue engineering and drug delivery settings. In this study, confined compression creep tests were performed on silk hydrogels, over a range of concentrations, to examine the phenomenological behavior of the gels under a physiological loading scenario. Based on the observed behavior, we show that the time-dependent response can be explained by a consolidation mechanism, and modeled using Biot's poroelasticity theory. Two observations are in strong support of this modeling framework, namely, the excellent numerical agreement between increasing load step creep data and the linear Terzaghi theory, and the similar values obtained from numerical simulations and direct measurements of the permeability coefficient. The higher concentration gels (8% and 12% w/v) clearly show a strain-stiffening response to creep loading with increasing loads, while the lower concentration gel (4% w/v) does not. A nonlinear elastic constitutive formulation is employed to account for the stiffening. Furthermore, an empirical formulation is used to represent the deformation-dependent permeability.