Hyperelastic constitutive modeling of hydrogels based on primary deformation modes and validation under 3D stress states

•Mechanical response of agarose depends on deformation mode and gel concentration.•A concentration dependent hyperelastic model is formulated for agarose gel.•Model is validated via 3D wedge indentation experiments.•Hyperelastic model calibration using a single deformation mode can lead to errors.•Multiple deformation modes (at least compression and tension) should be considered. In isotropic linear elasticity, a constitutive model calibrated using a single deformation mode (e.g., compression or tension or shear) is sufficient to describe a complex three-dimensional (3D) stress state. Such an approach, however, is likely inadequate for modeling hydrogels, which exhibit a nonlinear stress-strain response that varies significantly between deformation modes and is also sensitive to microstructure via gel concentration. In this study, a combined experimental and constitutive modeling framework is proposed for the development and validation of concentration-dependent 3D hyperelastic models for hydrogels. Agarose hydrogel in a concentration range of 0.4–4% w/v is chosen as the model material. Uniaxial compression, uniaxial tension, and simple shear (three primary deformation modes) experiments are conducted. The small strain elastic modulus-gel concentration relationships obtained from experiments are compared with those predicted by the molecular theory of rigid polymer networks (Jones-Marques theory) to identify the concentration range in which entropic elastic (hyperelastic) response dominates. In this range (1.5–4% w/v), four hyperelastic constitutive models are fit to the combined compression-tension-shear stress-strain data: Mooney-Rivlin, three-parameter generalized Rivlin, Gent, and Gent-Gent models. It is demonstrated that the generalized Rivlin model offers the best overall accuracy, and the variation of its model parameters with gel concentration is consistent with the Jones-Marques theory. The resulting concentration-dependent Extended Generalized Rivlin model is employed in finite element simulations of the non-homogeneous 3D stress state of wedge indentation. Simulated load versus depth and strain field predictions show very good agreement with experimental wedge indentation results. Finally, it is shown that a hyperelastic model calibrated using only a single deformation mode yields poor results for other primary and 3D deformations, and thus multiple primary deformation modes (preferably all three) should be considered. [Display omitted]