title: Stochastic hyperelastic constitutive laws and identification procedure for soft biological tissues with intrinsic variability.
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.
authors.affiliation: Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France.
authors.forename: B
authors.initials: B
authors.lastname: Staber
authors.affiliation: Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France. Electronic address: johann.guilleminot@u-pem.fr.
authors.forename: J
authors.initials: J
authors.lastname: Guilleminot
mesh_terms: D001921:Brain / Q000502:physiology; D003198:Computer Simulation; D004548:Elasticity; D006801:Humans; D008099:Liver / Q000502:physiology; D008954:Models, Biological; D013116:Spinal Cord / Q000502:physiology; D013269:Stochastic Processes; D013314:Stress, Mechanical; D066127:White Matter / Q000502:physiology
keywords: Biological material; Calibration; Constitutive law; Hyperelasticity; Information theory; Variability