The applications of elastic membrane range from determining the mechanical properties of biological cells by indentation tests to predicting the deformed shape of a large commercial tent structure. In this work, direct membrane theory and a particular Varga strain energy function are used to model the indentation and puncturing of an isotropic spherical elastic membrane containing a fluid with a rigid indenter. The balance laws are applied to obtain the governing differential equations and numerical shooting method is used to solve them. Furthermore, a global mode of failure is established by computing the energy stored at the punctured membrane and this value determines a critical value for the energy of the membrane beyond which the punctured state of the membrane is energetically preferred. An additional mode of failure is identified in which the membrane loses local convexity requirements and it corresponds to the local loss of elastic behavior of the membrane. / Graduate / 0548 / deris@Uvic.ca

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The applications of inflatable membrane structures are increasing rapidly in the various fields of engineering and science. The geometric, material, force and contact non-linearities complicate this subject further, which in turn increases the demand for computationally efficient methods and interpretations of counter-intuitive behaviors noted by the  scientific community. To understand the complex behavior of membranes in biological and medical engineering contexts, it is necessary to understand the mechanical behavior of a membrane from a physics point of view.  The first part of the  present work studies the pre-stretched circular membrane in contact with a soft linear substrate. Adhesive and frictionless contact conditions are considered during inflation, while only adhesive contact conditions are considered during deflation. The peeling of membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. It is observed that the pre-stretch is having a considerable effect on the variation of the energy release rate. In the second part, free and constrained inflation of a cylindrical membrane is investigated. Adhesive and frictionless contact conditions are considered between the membrane and substrate. It is observed that the continuity of principal stretches and stresses depend on contact conditions and the inflation/deflation phase. The adhesive traction developed during inflation and deflation arrests the axial movement of material points, while an adhesive line force created at the contact boundary is responsible for a jump in stretches and stresses at the contact boundary. The pre-stretch produces a softening effect in free and constrained inflation of cylindrical membranes. The third part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Both limit points and bifurcation points are observed on equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by an eigen-mode injection method. The occurrence of critical points and the stability of equilibrium branches are determined by perturbation techniques. The relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis. / <p>QC 20150227</p>

The aerodynamic behavior of wind tunnels with porous, flexible walls formed from tensioned Kevlar has been characterized and new measurement techniques in such wind tunnels explored. The objective is to bring the aerodynamic capabilities of so-called Kevlar-wall test sections in-line with those of traditional solid-wall test sections. The primary facility used for this purpose is the 1.85-m by 1.85-m Stability Wind Tunnel at Virginia Tech, and supporting data is provided by the 2-m by 2-m Low Speed Wind Tunnel at the Japanese Aerospace Exploration Agency, both of which employ Kevlar-wall test sections that can be replaced by solid-wall test sections. The behavior of Kevlar fabric, both aerodynamically and mechanically, is first investigated to provide a foundation for calculations involving wall interference correction and determination of the boundary conditions at the Kevlar wall. Building upon previous advancements in wall interference corrections for Kevlar-wall test sections, panel method codes are then employed to simulate the wind tunnel flow in the presence of porous, flexible Kevlar walls. An existing two-dimensional panel method is refined by examining the dependency of correction performance on key test section modeling assumptions, and a novel three-dimensional method is presented. Validation of the interference corrections, and thus validation of the Kevlar-wall aerodynamic performance, is accomplished by comparing aerodynamic coefficients between back-to-back tests of models carried out in the solid- and Kevlar-wall test sections. Analysis of the test results identified the existence of three new mechanisms by which Kevlar walls cause wall-interference. Additionally, novel measurements of the boundary conditions are made during the Kevlar-wall tests to characterize the flow at the boundary. Specifically, digital image correlation is used to measure the global deformation of the Kevlar walls under wind loading. Such data, when used in conjunction with knowledge of the pre-tension in the Kevlar wall and the material properties of the Kevlar, yields the pressure loading experienced by the wall. The pressure loading problem constitutes an inverse problem, and significant effort is made towards overcoming the ill-posedness of the problem to yield accurate wall pressure distributions, as well as lift measurements from the walls. Taken as a whole, this document offers a comprehensive view of the aerodynamic performance of Kevlar-wall test sections. / Ph. D. / Traditional wind tunnels, which measure the aerodynamic behavior of vehicles and components relevant to the aerospace industry, enclose some test object with solid walls and accelerate flow around the object. A new configuration has been developed which uses instead flexible, porous walls which are formed from tensioned Kevlar fabric. The original advantage of this configuration lies in its ability to produce high fidelity measurements of the acoustic signature of a model in a stream of air. This new configuration also has been emerging as tool for making the traditional measurements of aerodynamic behavior noted above. However, special considerations have to be made for the so-called Kevlar-wall test section because of the flexibility and porosity of the walls. This study focuses on understanding and exploiting Kevlar-wall wind tunnels with the hope to bring the aerodynamic measurement capabilities of Kevlar-wall test sections in-line with those of traditional solidwall test sections. The primary facility used for this purpose is the Stability Wind Tunnel at Virginia Tech, and supporting data is provided by the Low Speed Wind Tunnel at the Japanese Aerospace Exploration Agency, both of which employ Kevlar-wall test sections that can be replaced by solid-wall test sections. The behavior of Kevlar fabric, both aerodynamically and mechanically, is first investigated to provide a foundation for calculations of the effect of the Kevlar’s porosity and flexibility on the flow around a model in the test section. Building upon previous advancements in this area, computer simulations are then employed to predict the wind tunnel flow in the presence of porous, flexible Kevlar walls. An existing two-dimensional simulation is refined by examining the dependency of the simulation on key modeling assumptions, and a novel three-dimensional method is presented. Validation of the simulations’ effectiveness in providing accurate corrections for the Kevlar porosity and flexibility is accomplished by comparing measurements between back-to-back tests of models carried out in the solid- and Kevlar-wall test sections. Additionally, novel measurements of the deflection and pressure distributions over the Kevlar walls are made during the Kevlar-wall tests. Specifically, a three-dimensional camera imaging system is used to measure the deformation of the Kevlar walls under wind loading. Such data, when used in conjunction with knowledge of the pre-tension in the Kevlar wall, yields the pressure loading experienced by the wall. Taken as a whole, this document offers a comprehensive view of the aerodynamic performance of Kevlar-wall test sections.