Shear wave speeds in nearly-incompressible fibrous materials with two fiber families

An analytical and numerical investigation of shear wave behavior in nearly-incompressible soft materials with two fiber families was performed, focusing on the effects of material parameters and imposed pre-deformations on wave speed. This theoretical study is motivated by the emerging ability to image shear waves in soft biological tissues by magnetic resonance elastography (MRE). In MRE, the relationships between wave behavior and mechanical properties can be used to characterize tissue properties non-invasively. We demonstrate these principles in two material models, each with two fiber families. One model is a nearly-incompressible linear elastic model that exhibits both shear and tensile anisotropy; the other is a two-fiber-family version of the widely-used Holzapfel-Gasser-Ogden (HGO) model, which is nonlinear. Shear waves can be used to probe nonlinear material behavior using infinitesimal dynamic deformations superimposed on larger, quasi-static "pre-deformations."In this study, closed-form expressions for shear wave speeds in the HGO model are obtained in terms of the model parameters and imposed pre-deformations. Analytical expressions for wave speeds are confirmed by finite element simulations of shear waves with various polarizations and propagation directions. These studies support the feasibility of estimating the parameters of an HGO material model noninvasively from measured shear wave speeds.