Title

Interface problems in vascular mechanics and the mechanics of layered systems

Date of Award

2010

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical and Aerospace Engineering

Advisor(s)

Alan J. Levy

Keywords

Layered composites, Vascular mechanics, Atherosclerotic plaques

Subject Categories

Mechanical Engineering

Abstract

This dissertation investigates two novel interface problems arising in vascular mechanics and the mechanics of layered composite systems. In each of these problems, the interface is given distinct constitutive characterization in the form of nonlinear interface force-displacement jump relations which allows for phenomena such as interfacial debonding/decohesion, interface rupture and defect evolution to occur naturally without the addition of artificial "failure" criteria. This approach is applied to an investigation of a mechanism of atherosclerotic plaque rupture and, an exact, general analysis of debonding, decohesion and defect propagation and interaction in layered composite systems.

On the rupture of atherosclerotic plaques, a mechanism is proposed whereby rupture at low nominal loads occurs by brittle decohesion of the calcification/plaque cap interface followed by tearing of cap tissue. This mechanism is explored in model analyses in which an elastic matrix (the plaque cap ), of either half space or layer geometry, contains an embedded rigid spherical inclusion (the calcified cell ) that interacts with it through a nonlinear structural interface which mediates attachment by integrin receptor proteins. Equilibrium solutions to boundary value problems, accounting for rigid inclusion translation, are obtained from interfacial equations derived from the Boussinesq potentials for spherical domains. The solution indicates an abrupt/brittle character to the decohesion process similar to snap buckling of curved beams and shells. The size of the domain between the inclusion center and the free surface serves to determine the concentration of stress in that region. For a calcification close to the cap-luminal blood surface the abrupt unloading of the interface during brittle decohesion produces a spike in circumferential stress that, when exceeding the cap membrane strength, may precipitate cap tearing followed by the release of the thrombogenic necrotic core to the blood stream resulting in clotting and subsequent Acute Myocardial Infarction.

For the mechanics of layered composites, a general theory and computational tool is developed for systems consisting of an arbitrary number of linear elastic layers separated by distinct nonlinear decohesive interfaces and subject to general loads. Detailed features of debonding, along uniform and nonuniform (defective) straight interfaces, are analyzed by solving the governing interfacial integral equations obtained from the exact solution for a single linear elastic slab subject to arbitrary loading on its surfaces. The methodology allows for the investigation of both solitary defect as well as multiple defect interaction problems. The theory is applied in an analysis of a bilayer system, having a solitary defect or a defect pair, under both peeling and mixed mode loading configurations. An analysis of a trilayer system under uniform external loading is also carried out which reveals the complexity of interfacial separation phenomena. The theory is also applied to an analysis of a crack-like defect with the results compared to the classical static singular crack tip field.

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