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Title: Finite element modelling of biological connective soft tissues : application to the ligaments of the human knee
Author: Limbert, Georges
ISNI:       0000 0001 3610 2314
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 2001
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The research presented in this thesis addresses the issue of analytical and numerical aspects of the constitutive modelling of biological soft connective tissues. A general theoretical framework for the modelling of strongly anisotropic continuum fibre-reinforced composites at finite strain was first developed in order to provide solid theoretical bases for the formulation of a structurally-justified constitutive law describing the mechanical behaviour of ligaments. Then, a three-dimensional (3D) incompressible transversely isotropic hyperelastic law accounting for the key features of ligaments (incompressibility, anisotropy, nonlinear material, large deformations and rotations, very small bending stiffness, presence of residual stresses) was implemented into a commercial explicit finite element (FE) code. As applications of the material model, finite element analyses using experimental material data, were performed for simulating the behaviour of a human Anterior Cruciate Ligament (ACL) when the knee is subjected to a passive flexion. A second set of FE analyses was carried out in order to simulate the mechanical response of a 3D knee joint model (including the two collateral and the two cruciate ligaments) under anterior-posterior drawer forces. The originality of the theoretical framework for strongly anisotropic continuum fibre-reinforced composite at finite strain lie in the fact that the first and second derivatives of the strain energy function was performed without assuming any particular material symmetry or any kinematic constraints such as incompressibility. This provided the advantage of capturing all the possible mutual interactions of the matrix and the two families of fibres and encompassing all types of material symmetry. Describing material with particular symmetries or kinematic constraints or accounting for specific mechanical interactions is just a question of degenerating the equations involved. The incompressible transversely isotropic hyperelastic material implemented in the finite element code was properly validated against analytical solutions for homogeneous states of deformation and demonstrated robust and very good performance in the sensitivity analyses phase. The present research was motivated by the hypothesis that 3D isotropic models are not valid to represent the natural behaviour of ligaments. In fact, it was shown in a finite element model of the ACL, that highly unphysiological compressive and flexural stresses were generated as soon as a ligament undergoes compression in what should be the natural direction of the extended collagen fibres. The new anisotropic material model for the ACL was able to address successfully these severe limitations and by accounting for residual stress provided excellent agreement with quantitative experimental data such aa the resultant force developed in the ligament. The FE material model for soft tissue was also used to develop a global 3D model of the knee joint. For the first time, full 3D contact interactions between ligaments and bony structures was accounted for in simulated anterior-posterior drawer tests giving new insights in to the FE modelling of the knee. The FE model was sensitive enough to differentiate the mechanical response of an intact knee and that of an ACL-deficient knee. The primary restraining role of the ACL in anterior tibial drawer tests waa also confirmed.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available