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Original strain energy density functions for modeling of anisotropic soft biological tissue

Abstract : This thesis has focused on the construction of strain energy densities for describing the non-linear behavior of anisotropic materials such as biological soft tissues (ligaments, tendons, arterial walls, etc.) or fiber-reinforced rubbers. The densities we have proposed have been developed with the mathematical theory of invariant polynomials, particularly the Noether theorem and the Reynolds operator. Our work involved two types of anisotropic materials, the first with a single fiber family and the second with a four-fiber family. The concept of polyconvexity has also been studied because it is well known that it plays an important role for ensuring the existence of solutions. In the case of a single fiber family, we have demonstrated that it is impossible for a polynomial density of any degree to predict shear tests with a loading parallel and then perpendicular to the direction of the fibers. A linear polynomial density combined with a power-law function allowed to overcome this problem. In the case of a material made of a four-fiber family, a polynomial density allowed to correctly predict bi-axial tensile test data extracted from the literature. The two proposed densities were implemented in C++ language in the university finite element software FER by adopting a total Lagrangian formulation. This implementation has been validated by comparisons with reference analytical solutions exhibited in the case of simple loads leading to homogeneous deformations. More complex three-dimensional examples, involving non-homogeneous deformations, have also been studied.
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Submitted on : Friday, September 7, 2018 - 12:19:06 PM
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  • HAL Id : tel-01870267, version 1

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Renye Cai. Original strain energy density functions for modeling of anisotropic soft biological tissue. Biomechanics [physics.med-ph]. Université Bourgogne Franche-Comté, 2017. English. ⟨NNT : 2017UBFCA003⟩. ⟨tel-01870267⟩

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