On the Ability of Structural and Phenomenological Hyperelastic Models to Predict the Mechanical Behavior of Biological Tissues Submitted to Multiaxial Loadings

Abstract

Medical surgery is currently rapidly improving and requires modeling faithfully the mechanical behavior of soft tissues. Various models exist in literature; some of them created for the study of biological materials, and others coming from the field of rubber mechanics. Indeed biological tissues show a mechanical behavior close to the one of rubbers. But while building a model, one has to keep in mind that its parameters should be loading independent and that the model should be able to predict the behavior under complex loading conditions. In addition, keeping physical parameters seems interesting since it allows a bottom up approach taking into account the microstructure of the material. In this study, the authors consider different existing hyperelastic models based on strain energy functions and identify their coefficients successively on single loading stress-stretch curves. The experimental data used, come from a paper by Zemanek dated 2009 and concerning uniaxial, equibiaxial and plane tension tests on porcine arterial walls taken in identical experimental conditions. To achieve identification, the strain energy function of each model is derived differently to provide an expression of the Cauchy stress associated to each loading case. Firstly the parameters of each model are identified on the uniaxial tension curve using a least squares method. Then, keeping the obtained parameters, predictions are made for the two other loading cases (equibiaxial and plane tension) using the associated expressions of stresses. A comparison of these predictions with experimental data is done and allows evaluating the predictive capabilities of each model for the different loading cases. A similar approach is used after swapping the loading types. Since the predictive capabilities of the models are really dependent on the loading chosen to determine their parameters, another type of identification procedure is set up. It consists in adding the residues over the three loading cases during identification. This alternative identification method allows a better agreement between each model and the various types of experiments. This study evaluated the ability of some classical hyperelastic models to be used for a predictive scope after being identified on a specific loading type. Besides it brought to light some existing models which can describe at best the mechanical behavior of biological tissues submitted to various loadings.