Analytical and numerical modelling of thin functional layers

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Student thesis: Doctoral ThesisDoctor of Philosophy

Original languageEnglish
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Award date2018
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Abstract

The thesis deals with the study of thin layers and their function within larger
structures. Different thin intephases appearing in mechanics and biomechanics
are considered. The work aims at setting a manageable mathematical framework
in mechanical modelling. Analytical methods are provided in order to
achieve closed-form solutions and effective numerical procedures.

Cartilage, which reveals crucial in transmitting loads without friction along
the skeleton, is thoroughly investigated. Governing equations derived within
mixture theory are used for a biphasic description of the tissue. Inhomogeneity
and anisotropy are introduced and their effect on the global behavior of
the tissue is investigated. This is accomplished via integral transforms for
relatively small thickness of the layer and short-time asymptotics.

The model is extended to study the three-dimensional contact of cartilage
surfaces in the joint. The involved integro-differential equations are solved
in closed-form. Next, intra-articular pressurization is taken into account via
modelling the whole joint capsule. Implications for healthy degenerated and
tissues are discussed.

Lastly, cylindrical multilayer assemblies of layers are examined in the framework
of thermoelasticity. The general solutions for the single components are
arranged in a way to conveniently constitute a linear system. Perfect and
imperfect contact between the layers are considered. An efficient numerical
scheme is developed. Simulations are run with a special eye on ceramics.