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Article Dans Une Revue Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Année : 2018

Non‐affine fiber kinematics in arterial mechanics: a continuum micromechanical investigation

Résumé

There is growing experimental evidence for non-affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate-based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate-type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue.
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Dates et versions

hal-02004904 , version 1 (02-02-2019)

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Claire Morin, Stéphane Avril, Christian Hellmich. Non‐affine fiber kinematics in arterial mechanics: a continuum micromechanical investigation. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2018, 98 (12), pp.2101-2121. ⟨10.1002/zamm.201700360⟩. ⟨hal-02004904⟩
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