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International audience; The present paper proposes a new Strain Energy Function (SEF) for incompressible transversely isotropic hyperelastic materials, i.e. materials with a single fiber family. This SEF combines polyconvex invariants forming an integrity basis (Ta et al., 2014) in a polynomial and exponential form. Compared to a previous attempt for building a SEF based on the same invariants (Cai et al., 2016), we have reduced the number of material parameters from 23 to 10, without losing any accuracy on the numerical results. The 10 material parameters are identified by comparing the closed form solutions deriving from our model with experimental and numerical data extracted from the literature. These data concern uniaxial tension and shear tests, both parallel and transverse to the fiber direction (Ciarletta et al., 2011; Davis and De Vita, 2014) [3, 4], as well as shear calculations with 9 different fiber angles (Horgan and Murphy, 2017) [5]. Due to the variety of the considered situations, we have developed specific identification strategies based on: 1) the linear or nonlinear nature of the material parameters of the model; 2) the modeling of the free boundary conditions by a spectral approach.

International audience; Computational analysis of the nonlinear mechanical properties of anisotropic hyperelastic materials aims at a better understanding of its physiology and pathophysiology under different loading conditions. This has an important role in biomechanics, surgical, clinical diagnostic and design of medical devices. This study investigates the modeling of arterial tissues made of a four-fiber family by using an anisotropic hyperelastic model. This model is based on the theory of polynomial invariant and was implemented in the university finite element code FER. The convex property of the strain energy function is investigated as well as the positive definite nature of the tangent stiffness matrix used within the framework of a finite element analysis. This allows us to guarantee the invertibility of the linearized problem and the uniqueness of the solution computed at each step of the Newton–Raphson scheme used to solve nonlinear problems.

International audience; The present paper proposes a new Strain Energy Function (SEF) for modeling​ incompressible orthotropic hyperelastic materials with a specific application to the mechanical response of passive ventricular myocardium. In order to build our SEF, we have followed a classical strategy based on exponential functions, but we have chosen to work with polyconvex invariants instead of the standard ones. Actually, in the context of hyperelastic problems, the polyconvexity of the strain energy density is considered as a prerequisite for ensuring the existence of solutions. By selecting a set of polyconvex invariants, we demonstrate that our model can predict the experimental data with 6 different shear modes applied to passive ventricular myocardium.

International audience; We introduce in this paper a new hyperelastic model for the prediction of nonlinear mechanical properties of anisotropic hyperelastic materials under biaxial stretching. The proposed strain energy function (SEF) can be applied for understanding the nature of behavior laws for materials with four-fiber family structures, which has a large potential of applications, particularly in biomechanics, surgical and interventional therapies for peripheral artery disease (PAD). This SEF is built with a recent and new invariant system based on the mathematical theory of invariant polynomials. By recombining them in an appropriate manner, we demonstrate that it is possible to build a polyconvex integrity basis of invariants. Accuracy and reliability of the corresponding numerical model were validated by a comparison with experimental and numerical results extracted from Kamenskiy et al. (2014). 1 1We warmly thank Assistant Professor Kamenskiy to have kindly provided us the numerical data corresponding to the measurements included in These results concerned diseased superficial femoral (SFA), popliteal (PA) and tibial arteries (TA) from one patient under planar biaxial extension. For each kind of arteries tested with 5 combinations of different biaxial stretches, the predicted results of the proposed model and the experimental data are consistent. Our model includes 7 material parameters and their identification result in a single solution because of the linear form we have chosen for the SEF with respect to the material parameters.

International audience; The main goal of this study is to propose a practical application of a new family of transverse anisotropic invariants by designing a strain energy function (SEF) for incompressible fiber-reinforced materials. In order to validate the usability and creativeness of the proposed model, two different fiber-reinforced rubber materials under uniaxial and shear testing are considered. For each kind of material, numerical simulations based on the proposed model are consistent with experimental results and provide information about the effect of the new family of invariants in the construction of the SEF.