In this paper, the numerical simulation for nano-indentation is performed to measure time-dependent behavior of polymeric films. The possibility to extract the relaxed shear modulus of the polymer is evaluated using a rigid ball indenter. The viscoelastic behavior of the polymer was represented by the standard model. The effects of Poisson’s ratio are also discussed. / Singapore-MIT Alliance (SMA)

Magnetic Resonance Elastography (MRE) is a medical imaging technique used to generate a map of tissue elasticity. The resulting image is known as an elastogram, and gives a quantitative measure of stiffness in the examined tissue. The method is indirect; the elasticity, itself, is not measured. Instead, the physical response to a known stress is captured using magnetic resonance imaging, and is related to an elasticity parameter through a mathematical model of the tissue. In dynamic elastography, a harmonic stress is externally applied by a mechanical actuator, which is oriented to induce shear waves through the tissue. Once the system reaches a quasi-steady state, the displacement field is measured at a sequence of points in time. This data is the input to elasticity reconstruction algorithms. In this dissertation, the tissue is modelled as a linearly viscoelastic, isotropic continuum, undergoing harmonic motion with a known fundamental frequency. With this model, viscoelasticity is described by the complex versions of Lamé's first and second parameters. The second parameter, known as the complex shear modulus, is the one of interest. The term involving the first parameter is usually deemed negligible, so is ignored. The task is to invert the tissue model, a system of linear differential equations, to find the desired parameter. Direct inversion methods use the measured data directly in the model. Most current direct methods assume the shear modulus can be approximated locally by a constant, so ignore all derivative terms. This is known as the local homogeneity assumption, and allows for a simple, algebraic solution. The accuracy, however, is limited by the validity of the assumption. One of the purposes of MRE is to find pathological tissue marked by a higher than normal stiffness. At the boundaries of such diseased tissue, the stiffness is expected to change, invalidating the local homogeneity assumption, and hence, the shear modulus estimate. In order to capture the true shape of any stiff regions, a method must allow for local variations. Two new inversion methods are derived. In the first, a Green's function is introduced in an attempt to solve the differential equations. To simplify the system, the tissue is taken to be incompressible, another common assumption in direct inversion methods. Unfortunately, without designing an iterative procedure, the method still requires a homogeneity assumption, limiting potential accuracy. However, it is very fast and robust. In the second new inversion method, neither of the local homogeneity or incompressibility assumptions are made. Instead, the problem is re-posed in a quadratic optimization form. The system of linear differential equations is set as a constraint, and any free parameters are steered through quadratic programming techniques. It is found that, in most cases, there are no degrees of freedom in the optimization problem. This suggests that the system of differential equations has a fully determined solution, even without initial, boundary, or regularization conditions. The result is that estimates of the shear modulus and its derivatives can be obtained, locally, without requiring any assumptions that might invalidate the solution. The new inversion algorithms are compared to a few prominent, existing ones, testing accuracy and robustness. The Green's function method is found to have a comparable accuracy and noise performance to existing techniques. The second inversion method, employing quadratic optimization, is shown to be significantly more accurate, but not as robust. It seems the two goals of increasing accuracy and robustness are somewhat conflicting. One possible way to improve performance is to gather and use more data. If a second displacement field is generated using a different actuator location, further differential equations are obtained, resulting in a larger system. This enlarged system is better determined, and has improved signal-to-noise properties. It is shown that using data from a second field can increase accuracy for all methods.

Magnetic Resonance Elastography (MRE) is a medical imaging technique used to generate a map of tissue elasticity. The resulting image is known as an elastogram, and gives a quantitative measure of stiffness in the examined tissue. The method is indirect; the elasticity, itself, is not measured. Instead, the physical response to a known stress is captured using magnetic resonance imaging, and is related to an elasticity parameter through a mathematical model of the tissue. In dynamic elastography, a harmonic stress is externally applied by a mechanical actuator, which is oriented to induce shear waves through the tissue. Once the system reaches a quasi-steady state, the displacement field is measured at a sequence of points in time. This data is the input to elasticity reconstruction algorithms. In this dissertation, the tissue is modelled as a linearly viscoelastic, isotropic continuum, undergoing harmonic motion with a known fundamental frequency. With this model, viscoelasticity is described by the complex versions of Lamé's first and second parameters. The second parameter, known as the complex shear modulus, is the one of interest. The term involving the first parameter is usually deemed negligible, so is ignored. The task is to invert the tissue model, a system of linear differential equations, to find the desired parameter. Direct inversion methods use the measured data directly in the model. Most current direct methods assume the shear modulus can be approximated locally by a constant, so ignore all derivative terms. This is known as the local homogeneity assumption, and allows for a simple, algebraic solution. The accuracy, however, is limited by the validity of the assumption. One of the purposes of MRE is to find pathological tissue marked by a higher than normal stiffness. At the boundaries of such diseased tissue, the stiffness is expected to change, invalidating the local homogeneity assumption, and hence, the shear modulus estimate. In order to capture the true shape of any stiff regions, a method must allow for local variations. Two new inversion methods are derived. In the first, a Green's function is introduced in an attempt to solve the differential equations. To simplify the system, the tissue is taken to be incompressible, another common assumption in direct inversion methods. Unfortunately, without designing an iterative procedure, the method still requires a homogeneity assumption, limiting potential accuracy. However, it is very fast and robust. In the second new inversion method, neither of the local homogeneity or incompressibility assumptions are made. Instead, the problem is re-posed in a quadratic optimization form. The system of linear differential equations is set as a constraint, and any free parameters are steered through quadratic programming techniques. It is found that, in most cases, there are no degrees of freedom in the optimization problem. This suggests that the system of differential equations has a fully determined solution, even without initial, boundary, or regularization conditions. The result is that estimates of the shear modulus and its derivatives can be obtained, locally, without requiring any assumptions that might invalidate the solution. The new inversion algorithms are compared to a few prominent, existing ones, testing accuracy and robustness. The Green's function method is found to have a comparable accuracy and noise performance to existing techniques. The second inversion method, employing quadratic optimization, is shown to be significantly more accurate, but not as robust. It seems the two goals of increasing accuracy and robustness are somewhat conflicting. One possible way to improve performance is to gather and use more data. If a second displacement field is generated using a different actuator location, further differential equations are obtained, resulting in a larger system. This enlarged system is better determined, and has improved signal-to-noise properties. It is shown that using data from a second field can increase accuracy for all methods.

In this study, the mechanical properties of Cu-Zr binary bulk metallic glasses (BMG) were investigated at the nano-scale. The stable amorphous structures and corresponding energies of BMG structures are performed by density functional theory (DFT) calculation as reference data. This study will combine the Force-Matching (FM) method and Basin-Hopping (BH) method to develop a new method for fitting the Cu-Zr Tight-binding (TB) potential parameters. Moreover, the Bulk modulus, Shear modulus, Young's modulus and Poisson ratio of Cu46Zr54, Cu50Zr50 and Cu64Zr36 structures are calculated with the fitting TB parameters. In addition, the compression process of BMG materials is simulated by the Molecular Statics. The stress and strain are obtained to investigate the deformation mechanism of CuZr/Zr/CuZr nanolaminates at 0 and 45 inclined degree. Finally, we investigate the angle in the deformation process under different strain in the shear band, shear transformation zones (STZs) and force caused by the slip of the atomic distribution of TFMGs layer.

Soil properties (shear modulus and damping) are normally determined from laboratory tests. These tests provide both values of the shear modulus in the linear elastic range for very small levels of strain, and its variation with the level of strain. It has become more common to measure the maximum shear modulus at low levels of strain directly in the field, using geophysical techniques. The values obtained in situ can differ significantly in some cases from those determined in the laboratory, and a number of reasons and correction factors have been proposed in the literature to account for this variation. As a result, when in situ properties are available, it is normal to use these values for very low levels of strain, but still assume that the variation of the ratio G/Gmax (normalized shear modulus) with shear strain is the same as determined in the laboratory. Recently, tests have been performed using large vibrators (the Thumper and Tyrannosaurus Rex of the University of Texas at Austin) to determine soil properties in situ for larger strains, and the variation of G/Gmax obtained from these tests has been compared to that reported in the literature from lab tests. Observation indicates some generally good agreement, but also some minor variations. One must take into account, however, that in the determination of the shear modulus versus strain in the field from vibration records, a number of approximations are introduced. The objective of this work is to evaluate the accuracy of some the procedures used and to assess the validity of the simplifying assumptions which are made. For this purpose, a shear cone that would reproduce correctly the horizontal stiffness of a circular mat foundation on the surface of an elastic, homogeneous half space, was considered. The cone was discretized using both a system of lumped masses and springs and a finite difference, using second-order central difference formulation, verifying that in the linear elastic range the results were accurate. A number of studies were conducted next, increasing the level of the applied force and using nonlinear springs that would reproduce a specified G/Gmax vs. γ curve. Using a similar procedure to that used in the field tests, the shear wave velocity between hypothetical receivers and the levels of strain were determined. The resulting values of G/Gmax vs. γ were then compared with the assumed curve to assess the accuracy of the estimated values.

Södra DuraPulp is a relatively new eco-composite, made from natural wood fibers and polylactic acid (PLA), which comes from corn starch. Until now, there are only few applications for DuraPulp, mainly in the area of design. To find new fields of application, more knowledge about its mechanical material properties are of great interest.This study deals with characterizing the mechanical properties of DuraPulp in an analytical way by means of micromechanical modelling and evaluation with help of Matlab. The mechanical properties for PLA were taken from scientific literature. Not all properties of the wood fibers could be found in literature (particularly Poisson’s ratios were unavailable). Therefore, they partly had to be assumed within reasonable boundaries. These assumptions are later validated regarding their influence on the final product.Figures and tables were used to present and compare the in- and out-of-plane E-Moduli, shear moduli and Poisson’s ratios of DuraPulp. The calculated in-plane E-Moduli were then compared to those obtained from an earlier study, where DuraPulp was tested in tension. The results showed that experimental and analytical values are very similar to each other. / Södra DuraPulp är en relativt ny eco-komposit, tillverkat av naturliga trä fibrer och polylactic syra som kommer från majsstärkelser. I dagsläget finns det få användningsområden för DuraPulp, huvudsakligen används det inom design. För att expandera användningsområdet behövs det mer kunskaper angående de mekaniska egenskaperna för materialet. Studien handlar om att karakterisera de mekaniska egenskaperna för DuraPulp på ett analytiskt sätt i form av mikro-mekanisk modellering och evaluering med hjälp av Matlab. De huvudsakliga mekaniska egenskaperna för PLA kunde hämtas från flera vetenskapliga källor, men de motsvarande mekaniska egenskaperna för fibrer kunde inte alla valideras. Delvis antogs dem i rimliga gränser och deras inverkan validerades med hjälp av en parameter studie.Figurer och tabeller användes för att presentera och jämföra in- och ut-plan E-Moduler, skjuvmoduler och tvärkontraktionstalen av DuraPulp. De beräknade in-plan E-modulerna för DuraPulp jämfördes med motsvarande E-moduler från en tidigare studie där DuraPulp genomgick dragtest. Resultatet visade att analytiska och experimentella värden överensstämmer bra med varandra.

More commonly referred to as a quartz crystal microbalance (QCM), thickness-shear mode (TSM) quartz resonator devices utilize an acoustic wave to establish a bulk-detection mechanism prompting their utilization as gravimetric sensors with nanogram mass sensitivity and capability to measure various film property dynamics, due to variations in the system environment, of thin-films that are uniformly distributed across the resonator surface. The development of an absolute TSM-based nanobalance and an experimental technique using conventional TSM resonators for the real-time measurement of the change in the viscoelastic shear modulus and fractional free-hole volume of a poly(isobutylene) film due to the sorption of various organic vapors are presented in this thesis work. Development of an electrode-modified TSM quartz resonator that is responsive to nanogram mass loadings, while exhibiting a mass sensitivity profile that is independent of material placement on the sensor platform, is detailed in this thesis work. The resulting nanogram balance would greatly enhance the field of mass measurement and become useful in applications such as droplet gravimetry, the study of non-volatile residue (NVR) contamination in solvents. A ring electrode design predicted by an analytical theory for sensitivity distribution to achieve the desired uniform mass sensitivity distribution is presented in this work. Using a microvalve capable of depositing nanogram droplets of a polymer solution, and a linear stepping stage for radial positioning of these droplets across the sensor platform, measurements of the mass sensitivity distributions were conducted and are presented. The measurements agree well with theory. Further improvements are possible and are identified to achieve better uniformity and to reduce the instability in the resonant frequency of these devices. Additionally, droplet gravimetric results for NVR in methanol droplets using the modified TSM devices are presented, which compare well with determinations made by evaporation of larger volumes of the stock solutions. Storage modulus, G', loss modulus, G", and, consequently, the shear modulus, G (G=G'+jG"), of polymer and polymer/solvent systems were measured in this work using a TSM quartz resonator. The polymer poly(isobutylene) was spin-coated as a film of a few microns thickness on the surface of the TSM device and, upon inducing oscillation of the device at its resonance frequency (several mega-Hertz), the impedance characteristics were measured. In addition, the poly(isobutylene) film was exposed to known weight concentrations, up to 20%, of benzene, chloroform, n-hexane, and dichloromethane vapors diluted in nitrogen gas, and the impedance characteristics were measured. Data collected from the impedance analyzer were examined by modeling the polymer and polymer/solvent loaded TSM device with an electrical equivalent circuit and a mechanical perturbation model to reliably yield the shear modulus. Using a superposition theory and the shear modulus, the fractional free volume of the polymer/solvent systems were determined. These results correlate well with values found using the Vrentas-Duda free-volume (FV) theory. A novel experimental technique for measuring fractional free-hole volumes of polymer/solvent mixtures is established in this thesis work.

The primary objective of this research program was to investigate the effective modulus of elasticity and shear modulus of brick masonry walls under lateral load, and to to justify using the Jaeger and Mufti method to calculate the effective modulus of elasticity and shear modulus of brick masonry walls. The experimental program involved the testing of three unreinforced brick masonry walls under in-plane and vertical loads. Linear Variable Differential Transducers were used to record the horizontal and vertical displacements of the walls. The experimental results were used to evaluate the modulus of elasticity and the shear modulus of walls under flexure. The experimental results were compared to the finite element analysis results. It was found that the finite element analysis yields similar results to the experimental results. It was also found that the Jaeger and Mufti method to calculate effective modulus of elasticity and shear modulus of brick masonry walls is effective for design purposes.

The behavior of unsaturated soils depends heavily on material properties and soil conditions. In Geotechnical Engineering, compacted soils are frequently used as fill material, and quality control is vital to the construction process. There are few methods available to estimate the parameters associated with unsaturated soils based on field measurements, and a relationship between these factors could reduce testing time and lower construction costs. Undrained triaxial tests were performed on four clays representing a range of material properties in an effort to reach the maximum dry density, which provides the highest bearing capacity. Each clay was compacted at optimum moisture content, as well as wet and dry of optimum. Measurements were taken using the GeoGauge and shear wave velocities. An empirical approach was used to estimate the effect of a density gradient on soil suction. A relationship between the normal stress and matric suction produced a strong trend when plotted against a function of stiffness and the void ratio, which represents a density gradient. Another relationship between the GeoGauge and shear wave stiffness measurements was found, but no relationship with the material properties of the samples was observed, indicating that more in-depth research is needed to find a stronger relationship.

The primary objective of this research program was to investigate the effective modulus of elasticity and shear modulus of brick masonry walls under lateral load, and to to justify using the Jaeger and Mufti method to calculate the effective modulus of elasticity and shear modulus of brick masonry walls. The experimental program involved the testing of three unreinforced brick masonry walls under in-plane and vertical loads. Linear Variable Differential Transducers were used to record the horizontal and vertical displacements of the walls. The experimental results were used to evaluate the modulus of elasticity and the shear modulus of walls under flexure. The experimental results were compared to the finite element analysis results. It was found that the finite element analysis yields similar results to the experimental results. It was also found that the Jaeger and Mufti method to calculate effective modulus of elasticity and shear modulus of brick masonry walls is effective for design purposes.