The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.

Injuries to the head and neck are potentially the most severe injuries in humans, since they may damage the nervous system. In accidents, the cervical musculature stabilizes the neck in order to prevent injury to the spinal column and is also a potential site for acute muscle strain, resulting in neck pain. The musculature is consequently an important factor in the understanding of neck injuries. There is however a lack of data on muscle response and little is known about the dynamics of the individual muscles. In this thesis the numerical method of Finite Elements (FE) is used to examine the importance of musculature in accidental injuries. In order to study the influence of a continuum musculature, a 3D solid element muscle model with continuum mechanical material properties was developed. It was hypothesized that a 3D musculature model would improve the biofidelity of a numerical neck model by accounting for the passive compressive stiffness, mass inertia, and contact interfaces between muscles. A solid element representation would also enable the study of muscle tissue strain injuries. A solid element muscle model representing a 50th percentile male was created, based on the geometry from MRI, and incorporated into an existing FE model of the spine. The passive material response was modeled with nonlinear-elastic and viscoelastic properties derived from experimental tensile tests. The active forces were modeled with discrete Hill elements. In the first version of the model the passive solid element muscles were used together with separate active spring elements. In the second version the active elements were integrated in the solid mesh with coincident nodes. This combined element, called the Super-positioned Muscle Finite Element (SMFE), was evaluated for a single muscle model before it was incorporated in the more complex neck muscle model. The main limitation of the SMFE was that the serial connected Hill-type elements are unstable due to their individual force-length relationship. The instabilities in the SMFE were minimized by the addition of passive compressive stiffness from the solid element and by the decreased gradient of the force-length relation curve.  The solid element musculature stabilized the vertebral column and reduced the predicted ligament strains during simulated impacts. The solid element compressive stiffness added to the passive stiffness of the cervical model. This decreased the need for additional active forces to reproduce the kinematic response of volunteers during impact. The active response of the SMFE improved model biofidelity and reduced buckling of muscles in compression. The solid element model predicted forces, strains, and energies for individual muscles and showed that the muscle response is dependent on impact direction and severity. For each impact direction, the model identified a few muscles as main load carriers that corresponded to muscles generating high EMG signals in volunteers. The single largest contributing factor to neck injury prediction was the muscle active forces. Muscle activation reduced the risk of injury in ligaments in high-energy impacts. The most urgent improvements of the solid element muscle model concerns: the stability of the SMFE; the boundary conditions from surrounding tissues; and more detailed representations of the myotendinous junctions. The model should also be more extensively validated for the kinematical response and for the muscle load predictions. It was concluded that a solid muscle model with continuum mechanical material properties improves the kinematical response and injury prediction of a FE neck model compared to a spring muscle model. The solid muscle model can predict muscle loads and provide insight to how muscle dynamics affect spinal stability as well as muscle acute strain injuries. / QC 20100809

Purpose of this work is to provide a comprehensive picture of thin film (interconnect) and solid droplet surface evolution under the several external applied forces with anisotropic physical properties so that one can eventually be able to predict main reasons and conditions under which stability of surface is defined. A systematic study based on the self-consistent dynamical simulations is presented for the spontaneous surface evolution of an thin film and isolated thin solid droplet on a rigid substrate, which is driven by the surface drift diffusion induced by the anisotropic diffusivity, the anisotropic capillary forces (surface stiffness) and mismatch stresses under electron winding. The effect of surface free energy anisotropies (weak and strong (anomalous)) on the development kinetics of the Stranski-Krastanow island type morphology are studied. Although, various tilt angles and anisotropy constants were considered during simulations, the main emphasis was given on the effect of rotational symmetries associated with the surface Helmholtz free energy topography in 2D space. The investigations of dynamics of surface roughness on concurrent actions of the appliedelasto- and electro- static fields clearly indicate that applied misfit stress level is highly important effect on resultant surface form which may be smooth wave like or crack like. The droplet simulations revealed the formation of an extremely thin wetting layer during the development of the bell-shaped Stranski-Krastanow island through the mass accumulation at the central region of the droplet via surface drift-diffusion. The developments in the peak height, in the extension of in the wetting layer beyond the domain boundaries, and the change in triple junction contact angle, one clearly observes that these quantities are reaching certain saturation limits or plateaus, when the growth mode turned-off. Islanding differences for weak anisotropy constant levels and the strong (anomalous) anisotropy constant domains are discussed.

This work begins by establishing the necessary and sufficient conditions for hygrothermal stability of composite laminates. An investigation is performed into the range of coupling achievable from within all hygrothermally stable families. The minimum number of plies required to create an asymmetric hygrothermally stable stacking sequence is found to be five. Next, a rigorous and general approach for determining designs corresponding to optimal levels of coupling is established through the use of a constrained optimization procedure. Couplings investigated include extension-twist, bend-twist, extension-bend, shear-twist, and anticlastic. For extension-twist and bend-twist coupling, specimens from five- through ten-ply laminates are manufactured and tested to demonstrate hygrothermal stability and achievable levels of coupling. Nonlinear models and finite element analysis are developed, and predictions are verified through comparison with test results. Sensitivity analyses are performed to demonstrate the robustness of the hygrothermal stability and couplings to deviations in ply angle, typical of manufacturing tolerances. Comparisons are made with current state-of-the-art suboptimal layups, and significant increases in coupling over previously known levels are demonstrated.

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Two problems in the study of elastic filaments are considered.First, a reliable numerical algorithm is developed that candetermine the shape of a static elastic rod under a variety ofconditions. In this algorithm the governing equations are writtenentirely in terms of local coordinates and are discretized usingfinite differences. The algorithm has two significant advantages:firstly, it can be implemented for a wide variety of the boundaryconditions and, secondly, it enables the user to work with generalconstitutive relationships with only minor changes to thealgorithm. In the second problem a model is presented describingthe dynamics of an elastic tube conveying a fluid. First weanalyze instabilities that are present in a straight rod or tubeunder tension subject to increasing twist in the absence of afluid. As the twist is increased beyond a critical value, thefilament undergoes a twist-to-writhe bifurcation. A multiplescales expansion is used to derive nonlinear amplitude equationsto examine the dynamics of the elastic rod beyond the bifurcationthreshold. This problem is then reinvestigated for an elastic tubeconveying a fluid to study the effect of fluid flow on thetwist-to-writhe instability. A linear stability analysisdemonstrates that for an infinite rod the twist-to-writhethreshold is lowered by the presence of a fluid flow. Amplitudeequations are then derived from which the delay of bifurcation dueto finite tube length is determined. It is shown that the delayedbifurcation threshold depends delicately on the length of the tubeand that it can be either raised or lowered relative to thefluid-free case. The amplitude equations derived for the case of aconstant average fluid flux are compared to the case where theflux depends on the curvature. In this latter case it is shownthat inclusion of curvature results in small changes in some ofthe coefficients in the amplitude equations and has only a smalleffect on the post-bifurcation dynamics.

Following a head concussion the intracranial pressure increases due to the impact, which cannot be adequately relieved because of the stiffness of the skull. Popular strategies aimed at decompressing the head consist in the administration of osmotic agents and skull removal. The mechanical properties of bone can be affected by the administration of different solutions. If the malleability of skull is influenced by the osmotic agents that are administered to the patient then the pressure and volume in the intracranial cavity can also be modified following the treatment. In this thesis research, we hypothesize that administered osmotic agents can influence the mechanical properties of the skull, which can also impact the volume the cavity can hold and subsequently the pressure in the head. This premise was tested by modifying existing mathematical models compiled through two general MATLAB codes that allow the computation of a non-symbolic differential-algebraic initial value problem. Three main features were changed in comparison to current models: the skull's influence on the pressure and volume modulation was tested (inputs were obtained from skull tested under different solutions); pulsatile flow was accounted for on the creation and movement of cerebrospinal fluid; and the input on the mechanical behavior of the cranial vessels was accounted for through previously published continuum-mechanics vessel-behavior models. To complete the model, materials and mechanical properties were obtained through laboratory experiments as well as data collection from existing literature. From our bone test we were able to conclude that there are different factors that affect the mechanical properties of bone in various degrees. There is a mild statistical correlation (p-value 0.05) between the mechanical properties of bone obtained from different regions of the skull samples (2-14mm) and the DPBS and hDPBS solutions. Additionally there is a strong statistical difference (p-value 0.05) between the mechanical properties obtained from cross head speed (0.02, 0.002, and 0.004 (mm/s)) and solution variation (DI, DPBS and hDPBS). Finally, we were able to see that there seems to be a correlation between the mechanical properties of bone, the solution treatments and hypertension; although more test need to be developed to affirm this premise since our results are preliminary.

The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.

Thesis (M.S.)--Michigan State University. Mechanical Engineering, 2008. / Title from PDF t.p. (viewed on July 27, 2009) Includes bibliographical references (p. 49). Also issued in print.

Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004. / "January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynamics, Meshless Operators, Mlip (Multidimensional Lagrange Interpolating Polynomials), Flux Boundary Conditions, Radial Basis Functions Includes bibliographical references (58-59).