Approved for public release; distribution unlimited. / Current solar cell technology suffers low efficiencies in the commercial sector and cost prohibitive technology at higher efficiencies. This thesis investigates the possibility of a novel, alternate, avenue for the creation of solar power, which has the potential to be both cost effective and highly efficient. The approach converts solar energy into electrical energy via a MEMS device that utilizes spectrum-insensitive thermal absorption combined with power generation via the piezoelectric effect. The thesis investigates the underlying physics, materials needed, design requirements, computer modeling, optimization, and microfabrication process in the creation of such a device.

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The interface crack branching phenomena, including thermal effects, has been investigated by using complex variable method and Stroh's dislocation theory, extended to thermo-elasticity in matrix notation. As one of the most catastrophic failure modes in structures like laminated and sandwich composites in aerospace and marine construction, thin film in electronic packaging, rotators in high speed engine of aircraft and reactor in nuclear power station, the study of interface crack branching has become a topic not only having theoretical importance, but also having practical significance. A unified approach is presented to address the thermoelastic interface crack problems in dissimilar anisotropic bimaterial composites, and a compact closed form solution is formulated by analytical continuation principle of complex analysis. Employing the contour integral method, an explicit solution to the interaction between the dislocations and the interface crack is obtained. By modeling the branched portion as a continuous distribution of the dislocations, the thermoelastic interface crack branching problem is then converted to a set of semi-coupled singular integral equations and solved by Gauss-Jacobi integration schemes. The influence of material property mismatches between the two constituents and the thermal loading effects on the interface crack branching are demonstrated by extensive numerical simulation. Some useful criteria for predicting the interface crack branching growth and guidance for optimal composites design are suggested. Further, a contact model to eliminate the overlapping between the two surfaces of an interface crack is also proposed and some new parameters which could influence the interpenetrating phenomena are also discovered. The technique to extend the current method to three dimensional problems is also outlined. Furthermore, the C++ source code has been implemented to manipulate the complicated complex operations for numerically solving the singular integral equations in complex matrix form.

This thesis details an experimental study on the determination of the fracture parameters for a crack located at the interface between two dissimilar materials using the method of photoelasticity. The interface is potential1y an inherent weak spot of any composite material, structure"or adhesively bonded joint. Accurate description of the state of stress at the crack tip is required for strength prediction. The concept of the complex stress intensity factor is used to characterise the elastic crack tip stress field for an interface crack. Complex stress intensity factors and their moduli have been measured experimental1y for standard bimaterial crack geometries using the wel1 established technique of photo elasticity. Bimaterial specimens comprising aluminium al10y and epoxy resin components were used. This creates a large material mismatch at the interface and al10ws data to be col1ected from the epoxy component of the specimen using transmission photoelasticity. An automated ful1 field photoelastic technique was developed to significantly reduce the data col1ection time. The technique comprises elements from the approaches of three wavelength and phase stepping photoelasticity and is a significant improvement on techniques previously available. Stress intensity factors were determined by fitting a theoretical stress field solution for the bimaterial crack to the experimental data. A computational routine automatical1y selects the region of best fit between the experimental data and the theoretical solution. This data is then used to determine the complex stress intensity factor and its modulus value. In order to provide a robust fit between the experimental data and the theoretical field solution a weighting function was incorporated into the routine. The measured bimaterial stress intensity factors are compared with those determined experimental1y for equivalent homogeneous specimens made from epoxy resin. The differences between the two are then discussed. The experimental results agree with the wel1 known concept that tension and shear effects are inherently coupled at the crack tip. However, the effects of changing the load angle with respect to the interface also demonstrate that some contrasts exist with known numerical solutions.

The Reproducing Kernel Element Method (RKEM) implementation of the Fleck-Hutchinson phenomenological strain gradient theory in 1D, 2D and 3D is implemented in this research. Fleck-Hutchinson theory fits within the framework of Touplin- Mindlin theories and deals with first order strain gradients and associated work conjugate higher-order stress. Theories at the intrinsic or material length scales find applications in size dependent phenomena. In elasticity, length scale enters the constitutive equation through the elastic strain energy function which depends on both strain as well as the gradient of rotation and stress. The displacement formulation of the Touplin Mindlin theory involve diffrential equations of the fourth order, in conventional finite element method C1 elements are required to solve such equations, however C1 elements are cumbersome in 2D and unknown in 3D. The high computational cost and large number of degrees of freedom soon place such a formulation beyond the realm of practicality. Recently, some mixed and hybrid formulations have developed which require only C0 continuity but none of these elements solve complicated geometry problems in 2D and there is no problem yet solved in 3D. The large number of degrees of freedom is still inevitable for these formulation. As has been demonstrated earlier RKEM has the potential to solve higher-order problems, due to its global smoothness and interpolation properties. This method has the promise to solve important problems formulated with higher order derivatives, such as the strain gradient theory.

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This dissertation focuses on the development and application of numerical algorithms for solving compressible multiphase fluid-material interaction problems. The first part of this dissertation is motivated by the extraordinary shock-resisting ability of elastomer coating materials (e.g., polyurea) under explosive loading conditions. Their performance, however, highly depends on their dynamic interaction with the substrate (e.g., metal) and ambient fluid (e.g., air or liquid); and the detailed interaction process is still unclear. Therefore, to certify the application of these materials, a fluid-structure coupled computational framework is needed. The first part of this dissertation developes such a framework. In particualr, the hyper-viscoelastic constitutive relation of polyurea is incorporated into a high-fidelity computational framework which couples a finite volume compressible multiphase fluid dynamics solver and a nonlinear finite element structural dynamics solver. Within this framework, the fluid-structure and liquid-gas interfaces are tracked using embedded boundary and level set methods. Then, the developed computational framework is applied to study the behavior a bilayer coating–substrate (i.e., polyurea-aluminum) system under various loading conditions. The observed two-way coupling between the structure and the bubble generated in a near-field underwater explosion motivates the next part of this dissertation. The second part of this dissertation investigates the yielding and collapse of an underwater thin-walled aluminum cylinder in near-field explosions. As the explosion intensity varies by two orders of magnitude, three different modes of collapse are discovered, including one that appears counterintuitive (i.e., one lobe extending towards the explosive charge), yet has been observed in previous laboratory experiments. Because of the transition of modes, the time it takes for the structure to reach self-contact does not decrease monotonically as the explosion intensity increases. Detailed analysis of the bubble-structure interaction suggests that, in addition to the incident shock wave, the second pressure pulse resulting from the contraction of the explosion bubble also has a significant effect on the structure's collapse. The phase difference between the structural vibration and the bubble's expansion and contraction strongly influences the structure's mode of collapse. The third part focuses on the development of efficient solution algorithms for compressible multi-material flow simulations. In these simulations, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular class of methods in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation, such as the one used in the preceding parts of the dissertation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. This dissertation accelerates the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed. The performance of these acceleration methods is assessed using four example problems that exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times. / Doctor of Philosophy / This dissertation focuses on the development and application of numerical methods for solving multiphase fluid-material interaction problems. The first part of this dissertation is motivated by the extraordinary shock-resisting ability of elastomer coating materials (e.g., polyurea) under explosive loading conditions. Their performance, however, highly depends on their dynamic interaction with the underlying structure and the ambient water or air; and the detailed interaction process is still unclear. Therefore, the first part of this dissertation developes a fluid-structure coupled computational framework to certify the application of these materials. In particular, the special material property of the coating material is incorparated into a state-of-the-art fluid-structure coupled computational framework that is able to model large deformation under extreme physical conditions. Then, the developed computational framework is applied to study how a thin-walled aluminum cylinder with polyurea coating responds to various loading conditions. The observed two-way coupling between the structure and the bubble generated in a near-field underwater explosion motivates the next part of this dissertation. The second part of this dissertation investigates the failure (i.e., yielding and collapse) of an underwater thin-walled aluminum cylinder in near-field explosions. As the explosion intensity varies by two orders of magnitude, three different modes of collapse are discovered, including one that appears counterintuitive (i.e., one lobe extending towards the explosive charge), yet has been observed in previous laboratory experiments. Via a detailed analysis of the interaction between the explosion gas bubble, the aluminum cylinder, and the ambient liquid water, this dissertation elucidated the role of bubble dynamics in the structure's different failure behaviors and revealed the transition mechanism between these behaviors. The third part of this dissertation presents efficient solution algorithms for the simulations of compressible multi-material flows. Many problems involving bubbles, droplets, phase transitions, and chemical reactions fall into this category. In these problems, discontinuities in fluid state variables (e.g., density) and material properties arise across the material interfaces, challenging numerical schemes' accuracy and robustness. In this regard, a promising class of methods that emerges in the recent decade is to resolve the exact wave structure at material interfaces, such as the one used in the preceding parts of the dissertation. However, the computational cost of these methods is prohibitive due to the nested loops invoked at every mesh edge along the material interface. To address this issue, the dissertation develops four efficient solution methods, following the idea of exploiting special properties of governing equations and recycling previous solutions. Then, the acceleration effect of these methods is assessed using various challenging multi-material flow problems. In different test cases, significant reduction in computational cost (acceleration of 18 to 81 times) is achieved, without sacrificing solver robustness and solution accuracy.

The spatial patterns of bimaterial interfaces along the Parkfield section of the San Andreas Fault (SAF) and central section of the Calaveras Fault are systematically investigated with large data sets of near-fault waveforms. Different from the usage of direct P and S waves in traditional tomographic studies, a particular seismic phase named fault zone head wave (FZHW) is used to image the bimaterial fault interfaces. The results show clear variations of seismic velocities contrast both along-strike and along-depth directions in both regions, which is in general consistent with local geological setting at surface and existing 3D tomography results. In the Parkfield section of SAF, the result of velocity contrast is used to test the relationship between preferred rupture directions of M6 Parkfield earthquakes and bimaterial interface. Strong velocity contrast (~5-10%) near Middle Mountain (MM) could control the rupture directions of nearby earthquakes to SE, such as the case for 1966 M6 Parkfield earthquake. In comparison, weak velocity contrast (~0-2%) near the epicenter of the 2004 Parkfield M6 earthquake (i.e., Gold Hill) probably has no influence on controlling its rupture direction, which is consistent with the bilateral rupture of the 2004 Parkfield earthquake. In the central Calaveras Fault, a detailed analysis of the moveout between FZHWs and direct P waves revealed the existence of a complicated fault structure with velocity contrast increasing from NW to SE of station CCO. The high velocity contrast SE of station CCO could be caused by a low-velocity zone SE of station CCO. The spatio-temporal variations of seismic velocity around the central Calaveras Fault and its nearby region are investigated based on the waveform analysis of 333 repeating clusters following the 1984 ML6.2 Morgan Hill earthquake. Clear reduction of seismic velocity is shown for all repeating clusters immediately after the mainshock, followed by a logarithmic recovery. The coseismic change mostly occurs at shallow layers (top few hundred meters) for the region away from the rupture area of the mainshock, but extends much deeper around the rupture zone of the Morgan Hill earthquake. The estimated depth of the damage zone is up to 6 km in the fault based on the repeating clusters directly beneath station CCO. Finally, temporal changes around the Parkfield section of SAF are studied using recently developed ambient noise cross-correlation technique. The extracted daily empirical Green functions (EGFs) from 0.4-1.3 Hz noise records are used to estimate subtle temporal changes associated with large earthquakes from local to teleseismic distances. The results show clear coseismic reduction of seismic velocities after the 2004 M6 Parkfield earthquake, similar to the previous observation based on repeating earthquakes. However, no systematic changes have been detected for other four regional/teleseismic events that have triggered clear tremor activity in the same region. These results suggest that temporal changes associated with distance sources are very subtle or localized so that they could not be detected within the resolution of the current technique (~0.2%).

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Presented diploma thesis is concerned with problems of a stress singularity exponent and a generalized stress intensity factor determination, by dint the stress field in the vicinity of the stress concentrator can be consecutively determined. This task is possible to sectionalize into three parts. The first part summarizes basic information about linear anisotropic materials, deals with fundamentals of the linear elastic fracture mechanics and introduces its generalization to the case of the generalized stress intensity factors. The second part is dedicated to a special theory of anisotropic elasticity - Lekhnitskii-Eshelby-Stroh formalism (LES). Furthermore, a theory of the psi-integral is introduced, by dint the stress intensity factor is determined. The final part applies the LES theory and the psi-integral to the concrete material configuration of a crack on the bimaterial interface, a special example of a sharp bimaterial notch. By means of analytical-numerical algorithm in ANSYS and Silverforst FNT95 software the stress singularity exponents and generalised stress intensity factors are consecutively computed.