Thesis (Ph. D.)--University of Wisconsin--Madison, 1939. / Typescript. Includes abstract and vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

To date, elastographic imaging techniques such as magnetic resonance elastography (MRE) have primarily been considered isotropic material properties, despite the fact that most biological tissues tend to have some anisotropic qualities. In this thesis, a finite-element based orthotropic, incompressible material model is used as the basis for the in vitro MRE gelatin phantom. This study includes the use of biologically based orthotropic gelatin phantoms, with MRI data acquisition and boundary conditions suitable to describe the orthotropic material behavior. Fabricating a biological gelatin phantom using pineapple for MRE in vitro testing is a novel technique which was developed specially for this study. Multiple motion measurements from the pineapple gelatin phantom were made by applying directionally independent boundary conditions within the 85-125 Hz frequency range. Such multiple, orthogonal excitation data is needed to provide a complete description of the mechanical properties of this anisotropic phantom, given the potential for non-uniqueness of the reconstructed property estimates. Orthotropic image reconstructions were then carried out to map orthotropic elasticity properties in 3-D based on MR detected motion datasets captured from the pineapple gelatin phantom. The subzone based orthotropic incompressible reconstruction algorithm was based on the Conjugate Gradient optimization method, to gain computational efficiency, and used total volitional (TV) regularization techniques to constraint the solution process. The adjoint-residual method was utilized to improve the efficiency of the gradient descent based algorithm. The elasticity image reconstruction results presented for the orthotropic incompressible phantom are also correlated with isotropic property reconstructions for the same phantom.

An investigation was performed for live load forces applied to soil-steel structures under shallow backfill depths, specifically a long span deeply corrugated box culvert. The work was also relevant to other types of flexible buried structures and loading scenarios. The investigation involved the application of both a robust experimental testing process and the development of 3-D finite element models. Full scale live load tests, performed in Dorchester NB, were executed to obtain a large sample of experimental data. The testing program was designed specifically to fully characterize the structural response of a long span box culvert to CHBDC design truck live loads. The program included live load testing at six different backfill depths with 21 unique truck positions per lift, with instrumentation at four separate rings. The experimental data was used to assess and calibrate the finite element models being developed to predict structural effects. The finite element software package ADINA was used to model the test structure in 3-D. The basics of model development, such as element types, boundary conditions, loads, and other analysis options were discussed. An orthotropic shell modeling approach to accurately describe the corrugated plate properties was developed. A number of soil constitutive models, both linear and nonlinear, were examined and evaluated. The data obtained from experimental testing was compared to the results obtained by the finite element modeling and the various soil models were evaluated. A parametric study was performed examining the sensitivity of modeling parameters. The impact of various assumptions made regarding the model was quantitatively established. The thesis provided guidance on the 3-D modeling of soil-steel structures allowing future researchers to study the factors which were significant to their design and field applications.

Recent short pulse (femtosecond) laser experiments have shown the existence of a so called superelastic precursor for short time periods after shock wave formation. The superelastic precursor is characterised as having amplitude far greater than the Hugoniot Elastic limit. This work reviews the current orthotropic thermoelastic plastic-damage model developed at Cranfield University, which includes the ability to model high velocity, shock wave forming impacts. The current model is unable to reproduce the superelastic precursor. Recent methods of looking at plasticity are reviewed and model improvements are suggested to enable the Cranfield model to reproduce superelastic precursor waves. The methods investigated are both dislocation based as it is determined that it is necessary to model deformation on the microscale in order to achieve reproduction of phenomena on the timescales of the early stages of shock wave formation and propagation. The methods investigated are the so-called self-organisation of dislocations and a mobile and immobile dislocation method proposed by Mayer. The plasticity part of the model proposed by Mayer is suggested for further investigation, including implementation into the DYNA 3D hydrocode which contains the current Cranfield model, to numerically asses the models capabilities. Similar, the self-organisation model is put forward for further numerical analysis. Further, calculation of the continuum Cauchy stress using purely atomistic variables is investigated in the form of the virial stress. It is determined that the virial stress calculation is unsuitable for modelling shock waves, however an alternative atomistic stress calculation which is more suited to shock waves is discussed. It is proposed that this stress calculation could be used to investigate the stresses contained within the thin shock front.

Abstract Layered composite materials consisting of thin orthotropic layers offer for a designer many possibilities to tailor the structure: the behaviour and properties of the structure can be influenced not only by varying the geometry and thicknesses of the structure but also by varying the lay-up of the laminate. As new orthotropic materials having high specific strength and stiffness are used in structures, the tailoring is essential to utilize all the benefits of these materials. In this thesis tailoring and optimization of thermomechanical properties of layered composite structures are considered. The tailoring problemis formulated and solved as a constrained nonlinear optimization problem. Different types of global thermomechanical properties, such as stiffnesses, coefficients of thermal expansion and natural frequencies and buckling loads of composite plates, as well as layer-wise properties, such as stresses and strains in a certain lamina, are considered. Also, coupled thermalstructural problems are studied. When lay-up parameters, i.e. number of layers, and their orientations and thicknesses, are employed as design variables, global as well as layer-wise properties of the laminate can be considered. As relations between thermomechanical properties and lay-up parameters are highly nonlinear, optimization may suffer from various local optima. However, in tailoring the global minima or maxima are not the points of interest but rather the points of design space, where appropriate values for considered properties are achieved. In the thesis optimization of global thermomechanical properties is presented also by applying so-called lamination parameters as design variables. The lamination parameters are defined as integrals of the functions, which consist of sines and cosines of the lay-up angles of different layers multiplied by the powers of the thickness co-ordinate z, through the thickness of the laminate. Thus, information of the lay-up of the laminate can be compressed into these parameters and only twelve lamination parameters are needed to describe the behaviour of a common laminate. The use of these parameters as design variables is advantageous, because the number of parameters needed is small and often formulating a convex optimization problem is possible. After finding optimal lamination parameters, a procedure is needed to generate a lay-up corresponding to these parameters. Explicit equations are derived for generating lay-ups having optimal bending lamination parameters. For creating a laminate having both optimal in-plane and bending lamination parameters, a new optimization problem searching laminates having lamination parameters as close as possible to the optimal ones is formulated. In that problem, also layer-wise properties and restrictions of manufacturing are taken into account. Agenetic algorithmsearch is employed for solving that later problem as the value of the objective function can be computed efficiently. Also, often the thicknesses and orientations of different layers can have only discrete values, which can be handled easily in the GA search, where all design variables are discrete in character.

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The adhesive contact problems of a conical frustum punch indenting a transversely isotropic elastic half space and an orthotropic elastic half space are analytically studied in this thesis work. To solve the problem involving a transversely isotropic half space, the harmonic potential function method and the Hankel transform are employed, which lead to a general closed-form solution for the adhesive contact problem. For the case with an orthotropic half space, the problem of a point load applied on the half space is first solved by using the double Fourier transform method. The solution for the adhesive contact problem is then obtained through integrating the former solutions over the punch surface.

As the use of carbon fiber reinforced polymers (CFRP) increases in aerospace struc- tures it is important to use this material in an efficient manner such that both the weight and cost of the structure are minimized while maintaining its performance. To com- bat undesirable vibrational characteristics of a structure an optimization program was developed which takes advantage of the orthotropic nature of composite materials to maximize eigenfrequency bandgaps. The results from the optimization process were then fabricated and subjected to modal testing. The experiments show that local fiber angle optimization is a valid method for modifying the natural frequencies of a structure with the theoretical results generally predicting the performance of the optimized composite plates.

As the use of carbon fiber reinforced polymers (CFRP) increases in aerospace struc- tures it is important to use this material in an efficient manner such that both the weight and cost of the structure are minimized while maintaining its performance. To com- bat undesirable vibrational characteristics of a structure an optimization program was developed which takes advantage of the orthotropic nature of composite materials to maximize eigenfrequency bandgaps. The results from the optimization process were then fabricated and subjected to modal testing. The experiments show that local fiber angle optimization is a valid method for modifying the natural frequencies of a structure with the theoretical results generally predicting the performance of the optimized composite plates.

Bridges with orthotropic steel decks have been built across the world over the past 60 years because they provide high strength and stiffness at a relatively low cost. However, a number of these bridges have sustained fatigue fractures. The investigation described in this thesis was carried out in order to identify cost-effective fatigue crack mitigation techniques by using the deck surfacing to reduce the stresses in the steel deck. Epoxy asphalt with an expanded metal mesh was investigated with small- and large-scale laboratory tests. Finite element analyses were also performed. The small scale tests conducted at different temperatures and loading frequencies showed that asphalt stiffness increased with decreasing temperature and faster loading. The expanded metal mesh in the epoxy asphalt layer noticeably increased asphalt stiffness. In the large scale tests and finite element analyses, critical loading positions to cause stress concentrations at the fatigue prone rib-to-deck welded connections were determined with different tyre configurations. The stress reduction due to the deck surfacing was estimated for the critical loading positions. The full scale test specimen was subjected to actual truck tyres. With the effectiveness of mitigation techniques for fatigue cracks on orthotropic steel bridge decks known, a probability-based fatigue lifetime evaluation methodology using Monte Carlo simulation was developed. The deck surfacing effects with seasonal and hourly temperature variations were considered. The fatigue lifetime extension using the epoxy asphalt was quantified. For a particular bridge, cost-effective maintenance scenarios were investigated. A simple calculation method for fatigue lifetime was introduced for engineers or bridge owners to assist understanding of decision support tool concepts.