Premium absorbent paper products (e.g., two-ply towel and tissue) can achieve higher fluid holding capacity per unit dry weight by means of increasing their void volume per unit weight. In turn, high void volume can be attained by increasing the overall thickness of each ply through molding the paper into a three-dimensional ("mini-egg-crate") structure before drying it. This research investigates the effect of three types of parameters: mold geometrical, operational, and paper parameters. These variables are examined with respect to their effect on the resulting overall thickness. Because the experimental research is fundamental in nature, it employs molding structures of a simplified geometry (produced via rapid prototyping techniques) rather than the geometrically complex molding fabrics used commercially. A goal of the project is the understanding of the physics of the wet shaping process, in which vacuum is used to deform the wet paper web into the openings in the molding structure. Another goal is identification of limitations or boundaries of the wet shaping process (e.g., conditions for which "pinholes" occur in the paper). Supporting theoretical analysis of the shaping/molding problem is performed, to provide bases for correlating experimental data and for the optimization of molding geometrical parameters. The result of this study provides quantitative information for some variables that affect the final sheet thickness.

Current models of the modulus of elasticity, E , of concrete recommended by the American Concrete Institute (ACI) and the American Association of State Highway and Transportation Officials (AASHTO) are derived only for normally vibrated concrete (NVC). Because self consolidated concrete (SCC) mixtures used today differ from NVC in the quantities and types of constituent materials, mineral additives, and chemical admixtures, the current models may not take into consideration the complexity of SCC, and thus they may predict the E of SCC inaccurately. Although some authors recommend specific models to predict the E of SCC, they include only a single variable of assumed importance, namely the compressive strength of concrete, c f ′ . However there are other parameters that may need to be accounted for while developing a prediction model for the E of SCC. In this research, a Bayesian variable selection method is implemented to identify the significant parameters in predicting the E of SCC and more accurate models for the E are generated using these variables. The models have a parsimonious parameterization for ease of use in practice and properly account for the prevailing uncertainties.

Cancellous, or spongy, bone accounts for nearly 80% of the human skeleton’s internal surface area, despite comprising only 20% of its mass. It is made up of a network of struts and plates that provide lightweight internal support to mammalian bones. In addition, it often serves as the main interface between the skeletal system and implanted devices such as artificial hips, knees, and fracture fixation devices. However, hip arthroplasties can succumb to loosening of the implant due to bone resorption, which is thought to be caused by a mismatch in both apparent and real stiffness between the device and the surrounding bone. Many studies have attempted to determine the Young’s modulus of cancellous bone tissue, but the results are far from being in agreement. Reported values range from less than 1 to nearly 20 GPa. In addition, the small size of trabeculae has made dissection and testing a challenge. In this thesis, whole individual trabeculae from a bovine lumbar spine were tested in three-point bending to determine their Young’s modulus using custom-made equipment to fit a miniature single-axis testing device. The device itself was validated by testing materials with moduli ranging from 1 to 200 GPa. The structure of the cancellous bone and the morphology of the individual struts were determined using micro x-ray computed tomography (µXCT). Individual struts were manually isolated from slices made using a low-speed saw under constant lubrication and measured under a stereomicroscope. Samples exhibiting no machined surfaces (and thus deemed to be whole, or “uncut”) were compared to struts that had been cut by the saw during sectioning. Validation showed that the system was capable of determining the modulus of materials that were approximately five times stiffer than the expected cancellous modulus (copper, at 115 GPa) to within 10% of published values. This gave confidence in the results for bone. The modulus of the “uncut” specimens was found to be 15.28 ± 2.26 GPa, while the “cut” specimens had a significantly lower modulus (p = 1.665 × 10-6) at 2.63 ± 2.65 GPa. The lower modulus for “uncut” specimens may be due to microdamage that occurred during machining and dissection. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2010-08-26 00:03:49.732

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Residual moisture from incompletely dried aggregates would most likely remain in the Warm Mix Asphalt (WMA) due to its lower production and compaction temperature, resulting in harmful effects on field performance. Dynamic modulus has been recognized as a parameter that reflects the overall behavior of asphalt mixtures and possesses promising correlations with field performance. This study aims to investigate the effects of moisture susceptibility of WMA on dynamic modulus and simulate the field performance with the aid of Mechanistic-Empirical Pavement Design Guide (MEPDG) software. Four distinct sets of WMA specimens were prepared as follows: 1. fully dried aggregates without moisture conditioning; 2. fully dried aggregates with moisture conditioning; 3. incompletely dried aggregates without moisture conditioning; and 4. incompletely dried aggregates with moisture conditioning. Simple Performance Test (SPT) was employed to collect the raw data of dynamic modulus tests and master curves were constructed from the reduced data using Hirsch model. The results show that moisture can negatively influence the dynamic modulus values and moisture conditioning had more effect than residual moisture from incompletely dried aggregates. Two types of distress, fatigue cracking and rutting, were analyzed in the simulation. Moisture can significantly decrease the resistance against rutting and to a lesser extent, the resistance against fatigue cracking.

Traditional field seismic measurements have been performed for more than 50 years to determine the small-strain shear and constrained moduli of geotechnical materials under existing conditions. Field measurements to characterize the nonlinear response of the constrained modulus have received essentially no attention in the engineering community. This study was undertaken to characterize the in-situ response of the linear and nonlinear constrained moduli in one testing method. In this dissertation, a field method is presented which uses large shakers to impart vertical sinusoidal excitations directly above an embedded sensor array. This methodology essentially performs parametric studies on the constrained moduli of geotechnical materials in-situ over a wide range of axial strains. In this study, embedded sensor arrays at two different locations were constructed. A staged loading sequence was used to determine the constrained compression wave velocities between sensors in the linear, i.e. small-strain, and nonlinear strain ranges. Constrained moduli were determined using the mass density of the soil and the constrained compression wave velocities. The axial strains generated between sensors were estimated using a displacement-based method. At both sensor arrays, the method successfully measured in the field: (1) the variation of the small-strain constrained compression wave velocity with increasing confining pressure and (2) the effect of axial strain on the constrained moduli of soil in various states of stress. The field measurements indicate that, at lower levels of confining pressure, the constrained modulus increases slightly with increasing axial strain, but then decreases with increasing axial strain. However, in other cases, the constrained modulus increased with increasing axial strain and showed little or no tendency to reach a "peak" value. The nonlinear stress-strain behavior of the constrained modulus is quite complex and appears to be a function of several factors, including the amount of overconsolidation and cementation in the soil and the locations of the sensors in the array. Therefore, while the results of this study indicate that the proposed field method can be successfully used to investigate the constrained modulus, more work is required in this area to fully quantify the response of the constrained modulus in the nonlinear strain range. / text

In live acid solutions at concentrations of HCl namely 15-20 wt% HCl, elastic modulus remained quite low as compared to 10-12 wt% HCl concentrations. At 10 wt% HCl concentration, elastic modulus was 3.4 Pa observed whereas at 20 wt% HCl concentration, elastic modulus was 0.03 Pa. 0.5- 1.0 wt% concentrations of NaCl and CaCl2 showed negligible effect on the elastic modulus while 3-10 wt % concentrations, substantially reduced the elastic modulus. As little as 0.5 wt% Fe (III) concentration reduced elastic modulus quite significantly. In live acids, increase in temperature resulted in viscous modulus dominating the elastic modulus. Corrosion inhibitor reduced values of elastic modulus significantly, at 10 wt% HCl concentration elastic modulus dropped from 5.1 Pa to 3.4 Pa. Preparation of acid solution with sea water showed negligible effect at higher concentrations of HCl (> 10 wt% HCl) whereas at lower concentrations of HCl the elastic modulus fell sharply. For spent acid solutions, the elastic modulus at room temperature was quite low. Increase in temperature resulted in the increase in elastic modulus up to 130 F after which it decreased. At 190 - 205F and 18.8 rad/s, elastic modulus for 12 wt% HCl concentrations was 0.4 Pa whereas at 130 F, it was 2.25 Pa. At high temperatures (>130 F), the maximum elastic modulus shifted to higher concentrations of HCl namely 20 wt% HCl concentration. At 160 F, elastic modulus of 20 wt% HCl concentration at 18.8 rad/s was observed to be 2.6 Pa, whereas for 12 wt% HCl concentrations, it was 1.27 Pa. Throughout the HCl concentration and temperature range tested, viscous modulus dominated the elastic modulus for spent acid solutions. The effects of organic acids namely, formic and acetic acid, on the elastic modulus of viscoelastic surfactants have also been investigated.

An investigation into the intruder dynamics of dry dimensionless, frictionless discs in bidispersed, disordered systems is carried out using computer simulations. The velocity of an intruder particle driven under constant force is used as a tool to determine scaling of velocity as a function of packing pressure. Using these velocity for a range of pressures, $4 \times 10^{-7}\leq P \leq 4 \times 10^{-2}$. A universal scaling relation is proposed and plotted. The force required to cause the packing to yield to the driven intruder is determined and plotted as function of pressure. Power law exponents were extracted for the yielding force vs. the pressure. The extracted values were used to study the micro-rheology of the intruder particle. Grain scale characteristics are used to infer global elastic modulus properties.

Doctor of Philosophy / Department of Mathematics / Pietro Poggi-Corradini / This thesis contains six chapters. In the first chapter, the continuous and the discrete cases of p-modulus is introduced. We present properties of p-modulus and its connection to classical quantities. We also introduce use Arne Beurling's criterion for extremality to build insight and intuition regarding the modulus. After building an intuitive understanding of the p-modulus, we then proceed to switch perspectives to that of convex analysis. Using the theory of convex analysis, the uniqueness and existence of extremal densities is shown. We end this chapter with the introduction of the probabilistic interpretation of Modulus. In the second chapter, we introduce the Fulkerson duality. After defining the Fulkerson dual, we will investigate the blocking duality for different families of objects that the NODE research group has been studying and has been established. An important result that connects the Fulkerson dual and modulus is given at the end of this chapter. This important theorem will be used in proving one of the main results that [delta]p (introduced in Chapter 4) is a metric on graphs. The third chapter will discuss about metrics and ultrametrics on networks. Among these metrics, effective resistance is given special attention because the proof of [delta]p metric also serves as a new proof that effective resistance is a metric on graphs. We define effective resistance and give two different proves that show it is a metric, namely flows and the Laplacian. Two new families of metrics on graphs that arises through modulus are introduced in the fourth chapter. We also show how the two families are related as the d_p metric is viewed as a snowflaked version of the [delta]p metric. We end this chapter with some numerical examples that proves this connection and also serves as a set of plentiful examples of modulus calculations. Clutters and blockers is also another topic that is very much related to families of objects. While it has different rules and conditions, the study of clutters and blockers can give more insights to both modulus and clutters. We explore these relations in chapter 5. We provide some examples of clutters and blockers and finally reveal the relationship between the blocker and Fulkerson dual. Finally, in chapter 6, we end the thesis by presenting some of the open questions that we would like to explore and find answers in the future. In the second chapter, we introduce the Fulkerson duality. After defining the Fulkerson dual, we will investigate the blocking duality for different families of objects that the NODE research group has been studying and has been established. An important result that connects the Fulkerson dual and modulus is given at the end of this chapter. This important theorem will be used in proving one of the main results that delta_p (introduced in Chapter 4) is a metric on graphs. The third chapter will discuss about metrics and ultrametrics on networks. Among these metrics, effective resistance is given special attention because the proof of delta_p metric also serves as a new proof that effective resistance is a metric on graphs. We define effective resistance and give two different proves that show it is a metric, namely flows and the Laplacian. Two new families of metrics on graphs that arises through modulus are introduced in the fourth chapter. We also show how the two families are related as the d_p metric is viewed as a snowflaked version of the delta_p metric. We end this chapter with some numerical examples that proves this connection and also serves as a set of plentiful examples of modulus calculations. Clutters and blockers is also another topic that is very much related to families of objects. While it has different rules and conditions, the study of clutters and blockers can give more insights to both modulus and clutters. We explore these relations in chapter 5. We provide some examples of clutters and blockers and finally reveal the relationship between the blocker and Fulkerson dual. Finally, in chapter 6, we end the thesis by presenting some of the open questions that we would like to explore and find answers in the future.

Doctor of Philosophy / Department of Mathematics / Pietro Poggi-Corradini / This thesis contains four chapters. In the first chapter, the theory of continuous p-modulus in the plane is introduced and the background p-modulus properties are provided. Modulus is a minimization problem that gives a measure of the richness of families of curves in the plane. As the main example, we compute the modulus of a 2-by-1 rectangle using complex analytic methods. We also introduce discrete modulus on a graph and its basic properties. We end the first chapter by providing the relationship between connecting modulus and harmonic functions. This is the fact that computing the modulus of the family of walks from a to b is equivalent to minimizing the energy over all potentials with boundary values 0 at a and 1 at b. In the second chapter, we are interested in the connection between the continuous and the discrete modulus. We study the behavior of side-to-side modulus under some grid refinements and find an upper bound for the discrete modulus using the concept of Fulkerson duality between paths and cuts. These calculations show that the refinement will lower the discrete modulus. Since connecting modulus can also be computed by minimizing the Dirichlet energy of potential functions, we recall an argument of Jacqueline Lelong-Ferrand, that shows how refining a square grid in a ``geometric'' fashion, naturally decreases the 2- the energy of a potential. This monotonicity can be used to prove the convergence between continuous and discrete modulus. We first review the linear theory of discrete holomorphicity and harmonicity as provided by Skopenkov and Werness. Instead of reviewing their work in full generality, we present the outline of their arguments in the special case of square grids. Then use these results to prove the convergence between the continuous and discrete case. We believe that our method of proof generalizes to the full case of quadrangular grids that Werness studies. In the third chapter, we show how to generalize all our proofs for 2-modulus to the case of quadrangular grids with some geometric conditions on the lengths of edges and the angles between them. In the last chapter, a connection with potentials when p is not 2 is discussed in the square grid case. We study the behavior of side-to-side p-modulus under the same refinements as before and we find upper bound for the p-modulus, but only when p > 2. The rest of the chapter is dedicated to generalizing the results from Chapter 2 to the case 2 < p.