The study of instabilities in hyperelastic materials using ANM and FEM, first applications to bio mechanical problems.
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Asymptotic Numerical Method (ANM), based on a perturbation technique, is known to be an efficient continuation method for following equilibrium paths appearing in the resolution of nonlinear fluid or solid mechanical problems depending on a loading parameter [1]. In 2011, Nezamabadi [2] has explained how to apply ANM in the case of hyperelastic materials. Recently M. Potier-Ferry has presented a review paper [3] for the use of ANM in the case of hyperelasticity and plasticity. Following this work, the main features of the ANM algorithm will be presented. It has been implemented in the MATLAB platform and is dedicated for studying instability problems involving Neo-Hookean materials. First applications to bio mechanical topics will be presented. [1] B. Cochelin, N. Damil, M. Potier-Ferry, “Méthode Asymptotique Numérique ”, Hermès Lavoisier: Paris, France, 2007. [2] S. Nezamabadi, H. Zahrouni, J. Yvonnet, “Solving hyperelastic material problems by asymptotic numerical method”, Computational Mechanics, pp. 77-92, 2011. [3] M. Potier-Ferry, “Asymptotic numerical method for hypereleasticity and elastoplasticity: a review”; Proceeding of the Royal Society, vol. 480, issue 2285, march 2024.
