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The complete analysis of problems of solid mechanics must include the nonlinear effects of large deformations, inelastic material behaviour and changing boundary conditions. The finite element analysis of such problems using continuum finite elements is well established. However, the analysis of such problems using structural finite elements such as beams, plates and shells is still subject to restrictions which do not apply to continuum elements. The removal of these restrictions is important because (i) structural finite elements are widely used in current engineering practice (ii) the reduced number of variables associated with these elements leads to greater computational efficiency. The work carried out and reported in this thesis addresses the following areas of finite element analysis; the geometrically nonlinear analysis of two- and three-dimensional beams subject to arbitrarily large displacements and rotations; the elasto-plastic analysis of two- and three-dimensional beams using both multi-fibre and stress resultant approaches; the nonlinear analysis of two-dimensional reinforced concrete beams; the elasto-plastic analysis of shells using both the multi-layer and stress resultant approaches. A wide range of two- and three-dimensional problems have been analysed and the results reported. These problems cover a large number of two-dimensional beam, frame and arch problems including geometric and material nonlinearity. Results are compared with simple beam theory, other analytical solutions such as elliptic integrals, other finite element results and experimentation. Other problems analysed are three-dimensional beams with geometric and material nonlinearity, imperfect steel plates subject to large deformation elasto-plastic behaviour and two sample shell problems of practical application.

Defects, i.e. hot tears, macrosegragation, and pores, formed in metal castings are a result of stresses and strains in the solid-liquid mushy zone. Numerical simulation of solidification of deforming dendrite crystal promises to improve insight into the mechanical behavior of mushy zones under an applied load. The primary goal of this thesis is to develop numerical methodologies for performing solidification simulation of deforming dendrites. Such simulation encounters difficulties associated with the interface dynamics due to phase change or interaction among the dendrites, and large visco-plastic deformation applied to them. Phase-field simulation of dendritic solidification is promising for the treatment of the complex interface dynamics. Free energy based formulation allows the model to incorporate bridging and wetting phenomena occurring at grain boundaries through an extra energy term which arises from a mismatch of the crystallographic orientation. The particle method would be attractive to handle large inelastic deformation without suffering mesh entanglement. In order to investigate the effect of solid deformations on the evolving microstructure, the material point method with elasto-visco-plasticity constitutive model is developed to couple to a phase-field model of solidification. The changes in the crystallographic orientation of a growing dendrite crystal due to solid deformation are carefully accounted for through the coupling methodology. The developed numerical framework is applicable to the simulation for single and multiple crystals, and is capable of handling complex morphological change. The wide variety of validations and practical problems solved in this thesis demonstrates the capability of investigating deformation behavior of growing crystals.

acase@tulane.edu / Cell deformability is being recognized as an easily measurable indicator to differentiate different types of cells and detect diseased cells. A recent promising and advantageous technique to assess cell deformability is the cross-channel microfluidic deformability cytometry (DC). It uses a stretching extensional flow, in which each time an individual cell undergoes deformation. Using our three-dimensional computational algorithm for multiphase viscoelastic flow, known as VECAM, this study focuses on modeling the deformation of living cells in such microfluidic channels. Through the computational simulations, we first identified the central extensional flow region in the cross section of the channel, where cells are stretched due to mostly fluid momentum and resulting normal stresses. Our simulation data indicate that the range of deformability indices observed for human cells in DC experiments (from 1.5 to 2.3) corresponds to the range of cell elasticities from 3,000 to 15,000 Pa. We have also showed that both cell size and cortical tension have a much less effect on cell deformability than cell elasticity. The study further shows the cell oscillation in the extensional flow region caused by pressure imbalance in DC experiments does not affect much how long cell stays in this region and has a very limited impact on the measured cell deformability index. Finally, our study shows offset in both Y and Z directions can alter the results of the deformability measurement in a significant way. Our fully three-dimensional parallel computational algorithm is proven to realistically simulate cell movement and deformation in the cross-channel deformability cytometry. With the acquired simulation results, the computational study provides helpful insights and future guidance that are otherwise impossible to be obtained from the experimental data to the cytometry experiments. / 1 / Zhongyi Sheng

acase@tulane.edu / Cell deformability is being recognized as an easily measurable indicator to differentiate different types of cells and detect diseased cells. A recent promising and advantageous technique to assess cell deformability is the cross-channel microfluidic deformability cytometry (DC). It uses a stretching extensional flow, in which each time an individual cell undergoes deformation. Using our three-dimensional computational algorithm for multiphase viscoelastic flow, known as VECAM, this study focuses on modeling the deformation of living cells in such microfluidic channels. Through the computational simulations, we first identified the central extensional flow region in the cross section of the channel, where cells are stretched due to mostly fluid momentum and resulting normal stresses. Our simulation data indicate that the range of deformability indices observed for human cells in DC experiments (from 1.5 to 2.3) corresponds to the range of cell elasticities from 3,000 to 15,000 Pa. We have also showed that both cell size and cortical tension have a much less effect on cell deformability than cell elasticity. The study further shows the cell oscillation in the extensional flow region caused by pressure imbalance in DC experiments does not affect much how long cell stays in this region and has a very limited impact on the measured cell deformability index. Finally, our study shows offset in both Y and Z directions can alter the results of the deformability measurement in a significant way. Our fully three-dimensional parallel computational algorithm is proven to realistically simulate cell movement and deformation in the cross-channel deformability cytometry. With the acquired simulation results, the computational study provides helpful insights and future guidance that are otherwise impossible to be obtained from the experimental data to the cytometry experiments. / 1 / Zhongyi Sheng

Comprehensive fracture assessment is not an easy task as most fracture analyses rely on two-dimensional outcrops. A newly developed acquisition system of full resolution 3D Ground Penetrating Radar (GPR) and subsequent migration of the data allow, for the first time, to image fracture and deformation band networks in three dimensions. A full resolution GPR data set was acquired in the Madonna della Mazza quarry in the Maiella mountains, Italy. The quarry is cut into the Upper Cretaceous (Maastrichtian) Orfento Formation in the limb of an anticline. Combining 3D GPR and outcrop analysis reveals both the sedimentology and fracture characteristics in the quarry. The GPR data images the strata in more detail than what is visible in the quarry walls. For example, GPR data reveal a series of prograding bedsets that are interpreted as sub-aqueous dunes resulting from a unidirectional bottom or tidal current in the outer ramp environment. A fine-grained carbonate, lithofacies B, appears intermittently throughout the whole strata. In the massive grainstone beds extensive bioturbation destroyed the sedimentary structure and prevents the interpretation of the depositional process. The fracture development in the quarry is partly stratigraphically controlled. Deformation bands preferentially occur in the high porosity and high permeability massive grainstone unit, while stylolites are extensively developed in the thin-bedded packstone-grainstone lithofacies. The fracture analysis in the GPR data corroborates results of the outcrop analysis of previous workers. Performing a manual interpretation of the GPR data, faults with two dominant orientations (N-NW and E-W) were identified. The automated "Ant Tracking" analysis of the GPR data, however, revealed four dominant fracture orientations (N-NW, NW, W-NW, and EW). Furthermore, the automated ("Ant Tracking") 3D GPR analysis reveals a mechanical unit boundary; lithofacies C contains almost twice the density of deformation bands as the strata below. Integrating the outcrop analysis with the automated analysis of the 3D GPR data using "Ant Tracking" is essential for accurately quantifying the entire fracture population in the quarry. Total fracture diversity and abundance has previously been underestimated by 2D outcrop mapping and is also not completely depicted using manual interpretation of 3D GPR data.

While it is clear that myocardium responds to mechanical stimuli, it is unknown whether myocytes transduce stress or strain. It is also unknown whether myofibers maintain lateral connectivity or move freely over one another when myocardium is deformed. Due to the lack of information about the relationship between macroscopic and cellular deformations, we sought to develop an experimental method to examine myocyte deformations and to determine their degree of affinity. A set of protocols was established for specimen preparation, image acquisition, and analysis, and two experiments were performed according to these methods. Results indicate that myocyte deformations are non-affine; therefore, some cellular rearrangement must occur when myocardium is stretched.

Natural and hot isostatically pressed dolomite aggregates were experimentally deformed at effective pressures of Pe = 50 ?? 400 MPa, temperatures of 400 ?? 850??C, and strain rates of ε& = 1.2x10-4 s-1 to 1.2x10-7 s-1. Coarse- and fine-grained dolomite deformed at low temperature (T ≤ 700??C for coarse-grained natural dolomite, T < 700??C for fine-grained natural and synthetic dolomite) exhibit mechanical behavior that is nearly plastic; differential stresses are insensitive to strain rate, fitted either by a power law no⎟⎟⎠⎞⎜⎜⎝⎛−=??σσεε31&& with n values that range from 12 to 49 or an exponential law ([31exp )] σσαεε−=o&& with exponential law term α values from 0.023 to 0.079 MPa-1. Microstructures of samples deformed at low temperatures include mechanical twins, and undulatory extinction suggesting that twin glide and dislocation slip are the predominant deformation mechanisms. At high temperatures (T ≥ 800??C) flow strengths of coarse- and fine-grained dolomite depend more strongly on strain-rate and exhibit pronounced temperature dependencies. Microstructures of coarse-grained dolomite samples deformed at T ≥ 800??C include undulatory extinction and fine recrystallized grains suggesting that recovery and dynamic recrystallization contribute to dislocation creep at these conditions. By comparison with lower temperature deformation, mechanical twinning is unimportant. Fine-grained synthetic dolomite deformed at high temperature (T ≥ 700??C) exhibits nearly linear (Newtonian) viscous behavior, with n = 1.28 (??0.15) consistent with grain boundary (Coble) diffusion creep. At low temperatures (T ≤ 700??C) coarse-grained dolomite exhibits higher strengths at higher temperatures which cannot be described by an Arrhenius relation, while fine-grained dolomite strengths show little or no temperature dependence. At high temperatures (T ≥ 800??C), dislocation creep of coarse-grained dolomite can be described by a thermally activated power law ⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−=RTHno*31exp??σσεε&& with H*/n = 60 kJ/mol, or by an exponential law ()[]⎟⎟⎠⎞⎜⎜⎝⎛−−=RTHo*31expexpσσαεε&& with H*/α = 25447 kJ/mol. At high temperatures, diffusion creep of fine-grained synthetic dolomite can be described by ⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎠⎞⎜⎝⎛Ω=RTHdno*313exp??σσεε&& with H* = 280 ??45 kJ/mol. Taken together, the flow laws for coarse- and fine-grained dolomites constrain the high temperature conditions over which crystal plasticity, dislocation creep, and diffusion creep dominate.

The ill-posed problem of quantizing space-time is replaced by a more determined and well-posed problem of regularizing quantum dynamics. The problem is then to eliminate the Heisenberg singularity from quantum mechanics as economically as possible. The concepts of regular and singular groups are explained and the Heisenberg singularity defined. This singularity infests not only the theory of space-time, but also the Bose-Einstein statistics and the theory of the gauge fields and interactions. It is responsible for most of the infinities of present quantum field theory. The key new conceptual step is to turn attention from observables to "dynamicals", the observable-valued-functions of time which actually enters into the Heisenberg dynamical equations. The dynamicals have separate algebras from the algebra and Lie algebra of the observables. This reconception allows for the possibility of clock-system entanglement that is missing from the usual singular dynamics, and implied by the concept of quantum space-time. The dynamical Lie algebra and the resulting Lie group are regularized for an example system, the time-dependent isotropic harmonic oscillator of arbitrary finite dimension. The result is a quantize space-time, but also momentum-energy and every other dynamical variable in the theory. This method is readily extended to general dynamic quantum systems.

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