THESIS ANNOUNCEMENT

On the Energy Conserved in a Buckling Fung Hyperelastic

Cylindrical Shell Subjected to Torsion, Internal

Pressure, and Axial Tension

Ramsey Shadfan

ABSTRACT

A theoretical model is proposed for the buckling of a three-dimensional vein subjected to

torsion, internal pressure, and axial tension using energy conservation methods. The vein is

assumed to be an anisotropic hyperelastic cylindrical shell which obeys the Fung constitutive

model. Finite deformation theory for thick-walled blood vessels is used to characterize the vessel

dilation and thickness decrease in the pre-buckling state. The pre-buckling state is identified by

its midpoint and then perturbed by a displacement vector field dependent on the circumferential

and axial directions to define the buckled state. The total potential energy functional of the

system is extremized by minimizing the first variation with respect to the elements of the set of

all continuous bounded functions on ℝ3. The Euler-Lagrange equations form three coupled linear

partial differential equations with Dirichlet boundary conditions characterizing the buckling

displacement field under equilibrium. A second solution method approximates the first variation

of the total potential energy functional using a variational Taylor series expansion. The

approximation is minimized and combined with equations of equilibrium derived from elasticity

theory to yield a polynomial relating buckling eigenmodes, material parameters, geometric

parameters, and the critical angle of twist which induces buckling. Various properties of the total

potential energy functional specific to the problem are proved. Another solution method is

outlined using the first variation approximation and the basis of the kernel of the linear

transformation which maps buckling displacement amplitudes during static equilibrium.

DATE: August 1, 2018

TIME: 9:00 AM

LOCATION: FLN 4.01.20

CHAIR: Changfeng Gui, Ph.D.