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.

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.

The mechanics of a woven wire mesh material are investigated to characterize the elasto--plastic behavior of this class of materials under tensile conditions. The study focuses on a representative 316L stainless steel (3161 SS) 325x2300 twill-dutch woven wire mesh typically used as a fine filtration media in applications such as water reclamation, air filtration, and as a key component in swab wands used in conjunction with explosive trace detection (Em) equipment. Mechanical experiments and a 3-D finite element model (FEM) are employed to study the macro-scale and meso-scale mechanical behavior of the woven wire mesh under uniaxial tensile conditions. A parametric study of the orientation dependence of the mechanical response of this material ~ been carried out, relating material properties such as elastic modulus, yield strength, etc. to material orientation. Ratcheting type tensile tests are also performed in a similar orientation study, and an elementary damage model is presented for the woven wire mesh based on continuum damage mechanics (CDM). The meso-scale behavior of the wire mesh is studied via the finite element method, and observations are made relating wire scale conditions to macro-scale material behavior.

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The main objective of this study is to examine the three-dimensional surface crack problems in orthotropic materials subjected to mechanical or thermal loading. The cracks are modeled and embedded in the orthotropic material by considering semielliptical crack front geometry. In the model special elements are embedded in the crack front region, in this way it is possible to include crack tip singular fields along the crack front. Three-dimensional finite element analyses are conducted to obtain mode I stress intensity factors. The stress intensity factor is calculated by using the displacement correlation technique. In the analysis, collapsed 20-node iso-parametric elements are utilized to simulate strain singularity around the semi-elliptical crack front. The surface crack problem is analyzed under both mechanical and thermal stresses. In the case of mechanical loading, uniform tension and fixed grip tension loading cases are applied on the model. In thermal analysis, thermal boundary conditions are defined. Comparisons of the results generated to those available in the literature verify the developed techniques.

Composites are materials which cater to the present and future needs of many demanding industries, such as aerospace, as they are weight-sensitive for a given requirement of strength and stiff ness, corrosion resistant, potentially multi-functional and can be tailored according to the application. However, they are in particular difficult to join as they cannot be easily machined, without introducing damages which can eventually grow. Any structure is as strong as its weakest joint. Most of the joints belong to the category of mechanically-fastened joints and they pose enormous challenges in modeling due to contact phenomena, nonlinearity and stress concentration factors. It is therefore a necessity to construct an efficient model that would include all the relevant contact phenomena in the joints, as it has been pointed out in literature that damage typically initiates near the joint holes. The focus of this work is to describe the construction of an asymptotically-correct model using the Variational Asymptotic Method (VAM). Amongst its many potential applications, VAM is a well-established analytical tool for obtaining the stress and strain fields for beams and shells. The methodology takes advantage of the small parameter that is inherent in the problem, such as the ratio of certain characteristic dimensions of the structure. In shells and beams, VAM takes advantage of the dimension-based small parameter(s), thereby splitting the problem into 2-D + 1-D (for beams) and 1-D + 2-D (for shells), in turn offering very high computational efficiency with very little loss of accuracy compared to dimensionally unreduced 3-D models. In this work, the applicability of VAM is extended to two-dimensional (2-D) and three-dimensional (3-D) frictionless contact problems. Since a generalised VAM model for contact has not been pursued before, the `phantom0 step is adopted for both 2-D and 3-D models. The development of the present work starts with the construction of a 2-D model involving a large rectangular plate being pressed against a rigid frictionless pin. The differential equations governing the problem and the associated boundary conditions are obtained by minimizing the reduced strain energy, augmented with the appropriate gap function, by using a penalty method. The model is developed for both isotropic and orthotropic cases. The boundary value problem is solved numerically and the displacement field obtained is compared with the one obtained using commercial software (ABAQUSr) for validation at critical regions such as the contact surfaces. Banking on the validation of the 2-D model, a 3-D model with a pin and a finite annular cylinder was constructed. The strain energy for the finite cylinder was derived using geometrically exact 3-D kinematics and VAM was applied leading to the reduction in the strain energy for isotropic and orthotropic materials in rectangular and cylindrical co-ordinates. As in the 2-D case, the reduced strain energy, subject to the inequality constraint of the gap function, is minimized with respect to the displacement field and the corresponding boundary value problem is solved numerically. The displacements of the contact surface and the top surface of the annular cylinder are compared with those from ABAQUS and thus validated. The displacement fields obtained using the current 2-D and 3-D models show very good agreement with those from commercial finite element software packages. The model could be re ned further by using the gap function derived in this work and applying it to a plate model based on VAM, which could be explored in the future.

The hull is the most important structural part of any maritime vessel. It must be adequately designed to withstand the harsh sailing environmental conditions and associated forces. In the past, the basic material used to manufacture the ship hull was wood, where the hull was usually shaped as cylindrical wooden shanks. In the present, hull designs have developed to steel columns or stiffened panels that are made of different types of materials. Panels that are stiffened orthogonally in two or more directions and have nine independent material constants are defined as orthotropic panels, and they achieve high specific strength. This thesis presents the effect of different patch orientations on the resulting strain and stress concentrations at the area of interaction between the panel and the patch. As it is known, the behavior of stiffened plates is affected by several important parameters, e.g., length to width ratio of the panel, stiffener geometry and spacing, aspect ratio for plates between stiffeners, plate slenderness, von Mises stresses, initial distortions, boundary conditions, and type of loading. A finite element model of the ship hull has been developed and run on ABAQUS (commercially available finite element software). The stiffened panel and patch are modeled as equivalent orthotropic plates made of steel. The panel edges are considered to be simply supported, and uniaxial tension was applied to the equivalent stiffened panel in addition to the lateral pressure (from water interaction). The developed model successfully predicted the optimal orientation of the panel for maximum stress concentration reduction. Moreover, in order to minimize the severe conditions caused by the mismatch that occurs if the material properties of the patch and the panel are the same during the patching process, it is necessary to stiffened the patch more than the panel. The developed model also suggested that an isotropic layer be added at the interaction to decrease the severity of arising stresses.