No abstract

In this work, we address the constitutive modeling, in a probabilistic framework, of the hyperelastic response of soft biological tissues. The aim is on the one hand to mimic the mean behavior and variability that are typically encountered in the experimental characterization of such materials, and on the other hand to derive mathematical models that are almost surely consistent with the theory of nonlinear elasticity. Towards this goal, we invoke information theory and discuss a stochastic model relying on a low-dimensional parametrization. We subsequently propose a two-step methodology allowing for the calibration of the model using standard data, such as mean and standard deviation values along a given loading path. The framework is finally applied and benchmarked on three experimental databases proposed elsewhere in the literature. It is shown that the stochastic model allows experiments to be accurately reproduced, regardless of the tissue under consideration.

This paper is devoted to the modeling of compressible hyperelastic materials whose response functions exhibit uncertainties at some scale of interest. The construction of parametric probabilistic representations for the Ogden class of stored energy functions is specifically considered and formulated within the framework of Information Theory. The overall methodology relies on the principle of maximum entropy, which is invoked under constraints arising from existence theorems and consistency with linearized elasticity. As for the incompressible case discussed elsewhere, the derivation essentially involves the conditioning of some variables on the stochastic bulk and shear moduli, which are shown to be statistically dependent random variables in the present case. The explicit construction of the probability measures is first addressed in the most general setting. Subsequently, particular results for classical Neo‐Hookean and Mooney‐Rivlin materials are provided. Salient features of the probabilistic representations are finally highlighted through forward Monte‐Carlo simulations. In particular, it is seen that the models allow for the reproduction of typical experimental trends, such as a variance increase at large stretches. A stochastic multiscale analysis, where uncertainties on the constitutive law of the matrix phase are taken into account through the proposed approach, is also presented.