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We review nine invariant and dispersion-type anisotropic hyperelastic constitutive models for soft biological tissues based on their fitting performance to experimental data from three different human tissues. For this, we used a hybrid multi-objective optimization procedure. A genetic algorithm is devised to generate the initial guesses followed by a gradient-based search algorithm. The constitutive models are then fit to a set of uniaxial and biaxial tension experiments conducted on tissues with differing fiber orientations. For the in silico investigation, experiments conducted on aneurysmatic abdominal aorta, linea alba, and rectus sheath tissues are utilized. Accordingly, the models are ranked with respect to an objective normalized quality of fit metric. Finally, a detailed discussion is carried out on the fitting performance of each model. This work provides a valuable quantitative comparison of various anisotropic hyperelastic models, the findings of which can aid those modeling the behavior of soft tissues in selecting the best constitutive model for their particular application.

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This contribution presents a novel constitutive model for rate-dependent response of the passive myocardium. As a first step, we performed a comparative study on dispersion-type anisotropic hyperelastic constitutive models [1-3] and assessed performance of various density distribution functions by fitting to experiments conducted on three distinct tissues [4]. Next, we proposed an angular integration type anisotropic viscoelastic constitutive model that uses bivariate von-Mises distribution function to capture fiber dispersion in passive myocardium. The baseline hyperelasticity is described by a generalized structure tensor formulation proposed by GASSER ET AL. [1]. The non-equilibrium part of the model utilizes a quadratic free energy function in the logarithmic strain space and a power-type nonlinear evolution equation in orientation directions. The overstress response is then obtained by the numerical integration over the unit sphere by making use of 21 quadrature points. The proposed model parameters are obtained from cyclic triaxial shear and triaxial shear relaxation experiments on human passive myocardium [5].