"In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric. In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field. In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs. Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples. The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction."

Propagation of cracks in functionally graded materials (FGMs) under cyclic loading was investigated via experiments and finite element (FE) analysis. Alumina-epoxy composites with an interpenetrating-network structure and tailored spatial variation in composition were produced via a multi-step infiltration technique. Compressed polyurethane foam was infiltrated with alumina slip. After foam burn-out and sintering, epoxy was infiltrated into the porous alumina body. Non-graded specimens with a range of compositions were produced, and elastic properties and fatigue behaviour were characterised. An increase in crack propagation resistance under cyclic loading was quantified via a novel analytical approach. A simulation platform was developed with the commercial FE package ANSYS. Material gradient was applied via nodal temperature definitions. Stress intensity factors were calculated from nodal displacements near the crack-tip. Deflection criteria were compared and the local symmetry criterion provided the most accurate and efficient predictions. An automated mesh-redefinition algorithm enabled incremental simulation of crack propagation. Effects of gradient and crack-geometry parameters on crack-tip stresses were investigated, along with influences of crack-shape, crack-bridging, residual stresses and plasticity. The model provided predictions and data analysis for experimental specimens. Fatigue cracks in graded specimens deflected due to elastic property mismatch, concordant with FE predictions. In other FGMs, thermal or plastic properties may dominate deflection behaviour. Weaker step-interfaces influenced crack paths in some specimens; otherwise effects of toughness variation and gradient steps on crack path were negligible. Crack shape has an influence, but this is secondary to that of elastic gradient. Cracks in FGM specimens initially experienced increase in fatigue resistance with crack-extension followed by sudden decreases at step-interfaces. Bridging had a notable effect on crack propagation resistance but not on crack path. Similarly, crack paths did not differ between monotonic and cyclic loading, although crack-extension effects did. Recommendations for analysis and optimisation strategies for other FGM systems are given. Experimental characterization of FGMs is important, rather than relying on theoretical models. Opportunities for optimization of graded structures are limited by the properties of the constituent materials and resultant general crack deflection behaviour.

This study introduces a multiscale model for analyzing nonlinear thermo-viscoelastic responses of particulate composites. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermal and mechanical properties and time-dependent response of the composites. The particle and matrix constituents are made of isotropic homogeneous viscoelastic bodies undergoing small deformation gradients. Perfect bonds are assumed along the sub-cell⁰́₉s interfaces. The coupling between the thermal and mechanical response is attributed to the dissipation of energy due to the viscoelastic deformation and temperature dependent material parameters in the viscoelastic constitutive model. The micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the sub-cells. The effective mechanical properties and coefficient of thermal expansion are derived by satisfying displacement- and traction continuities at the interfaces during the thermo-viscoelastic deformations. The effective thermal conductivity is formulated by imposing heat flux- and temperature continuities at the subcells⁰́₉ interfaces. The expression of the effective specific heat at a constant stress is also established. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic materials is developed. The algorithm is then incorporated within each sub-cell of the micromechanical model together with the macroscopic energy equation to determine the effective coupled thermoviscoelastic response of the particulate composite. The numerical formulation is implemented within the ABAQUS, general purpose displacement based FE software, allowing for analyzing coupled heat conduction and deformations of composite structures. Experimental data on the effective thermal properties and time dependent responses of particulate composites available in the literature are used to verify the micromechanical model formulation. The multiscale model capability is also examined by comparing the field variables, i.e., temperature, displacement, stresses and strains, obtained from heterogeneous and homogeneous composite structures, during the transient heat conduction and deformations. Examples of coupled thermoviscoelastic analyses of particulate composites and functionally graded structures are also presented. The present micromechanical modeling approach is found to be computationally efficient and shows good agreement with experiments in predicting the effective thermo-mechanical response of particulate composites and functionally graded materials. Our analyses forecast a better design for creep resistant and less dissipative structures using particulate composites and functionally graded materials.

The thesis consists of an introductory part and three self-contained papers. Paper [I] studies the determinants of the differences in expenditure on services for functionally impaired individuals among municipalities in Sweden. A spatial autoregressive model is used in order to test whether the decisions on the expenditure level in a neighboring municipality affect the municipality’s own expenditure. The results show of spatial interaction among neighbors, possible due to mimicking. However, when controlling for differences among counties there is no evidence of spatial interaction. Therefore, the positive interaction first found can be interpreted either as a result of differences in the way county councils diagnose individuals or due to interaction among the neighbors in the same county. Paper [II] takes advantage of a new intergovernmental grant in two ways. First, the grant is used to study the effect on municipal spending related to the grant. Second, the grant is used to test a hypothesis of spatial interaction among municipalities due to mimicking behavior. The data used pertains to the periods before and after the introduction of the grant. A fixed-effects spatial lag model is used to study the spatial interactions among municipalities. The results show that before the grant, municipalities interact with their neighbors when setting the expenditure level, while there is no evidence of interaction in the second period. This would support the hypothesis that the grants provide information to the municipalities and the need for mimicking diminishes with the grant. Paper [III] examines whether local public expenditures on services to functionally impaired individuals crowd out other local public expenditures in Sweden. The hypothesis is tested on five different spending areas using a two-stage least squares (2SLS) fixed-effects model. While the results give no support for crowding out in the areas of social assistance, culture & leisure, and childcare & preschool, a negative relationship on spending for elderly & disabled care and on spending for education is found, suggesting that crowding out indeed occurs within the municipal sector. The negative relationships are significant both in a statistical and an economic sense.

No description available.

The objective of this study is to determine stress intensity factors (SIFs) for a crack in a radially graded FGM layer on a substrate. Functionally graded coating with an edge crack perpendicular to the interface and a homogeneous substrate are bonded together. In order to make the problem analytically tractable, geometry is modeled as an FGM strip attached to a homogeneous layer. Introducing the elastic foundation underneath the homogeneous layer, an FGM coating on a thin walled cylinder can be modeled. At first, governing equations are obtained from stress displacement and equilibrium equations. Then using an assumed form of solution in terms of Fourier Transforms for displacements and applying the boundary conditions, a singular integral equation is obtained for the mode-I problem. Solving this singular integral equation numerically, stress intensity factors are obtained as functions of crack length, strip thicknesses and inhomogeneity parameter.

In some applications the stress across the entire cross-section of a component is not uniform but varies with position. For example, maximum shear stress is highest at the inner surface of a thick-walled cylinder subjected to uniform internal pressure and it decreases continuously towards the outer surface. In such applications it would be more appropriate for the component, too, to have varying strength across the cross-section matching with the stress profile it is subjected to. The present work deals with obtaining such a functionally graded material (FGM), characterizing it and testing its mechanical properties in compression. Differential aging heat treatment was used to produce the functionally graded material in a precipitation hardenable Al-4.6%Cu alloy by changing the microstructure. Temperature gradient furnace was used to achieve the gradation in microstructure from one end of the sample to the other end by differential aging of the solution treated sample. Mechanical properties can be varied in any precipitation hardenable alloy by means of producing various precipitates, which will form during the aging sequence. In Al-4.6%Cu alloy one end of the solution treated sample was aged for 38 hours at 170°C and the other end at 70°C by means of a temperature gradient furnace in which the coil density varies along the axis of the furnace. Thus we achieved a difference in mechanical properties from 70°C side to 170°C side as the precipitation during differential aging varied from GP zones at one end to θ' precipitate at the other end. Characterization was done on isothermally aged samples and in FGM using XRD (X-ray diffraction) and TEM (Transmission Electron Microscopy). XRD result showed that the final equilibrium precipitate θ was not formed in any of the heat-treated samples. TEM result showed the various precipitation sequences from GP zones to θ' in the isothermally aged samples and the same was confirmed in the gradient sample by cutting the samples form 70°C side towards the 170°C side and doing TEM on each sample. The properties of FGM in compression were studied using a 9mmx9mmxl8mm-compression sample using DARTEC machine and it was compared with those of isothermally aged samples. For 70°C the 0.2% proof stress was 141MPa and for 170°C it was 226MPa. The corresponding ductility values at the point of inflection on the engineering stress-strain curve for 70°C sample was higher (33%) than the 170°C (22%) sample. For the gradient sample it gave a proof stress of 163MPa and a ductility value of 30%.

Thesis (M.S. in M.S.E.)--School of Materials Science and Engineering, Georgia Institute of Technology, 2004. Directed by Rober Narayan. / Includes bibliographical references (leaves 85-92).

This study involved families of young children with autism spectrum disorders to examine the feasibility of implementing an adapted version of the school-based Prevent-Teach- Reinforce (PTR) model. This research included two families who developed and implemented the intervention for their children in collaboration with the researcher. The PTR manual was modified for use in a family context. The PTR intervention was tested using a multiple baseline design across routines. Procedural fidelity was assessed during training and coaching, as well as family implementation fidelity and social validity. To examine the potential efficacy of the adapted PTR intervention, the children’s target problem behavior and functionally equivalent alternative behavior were measured using video observation across experimental conditions including a generalization probe. Results indicated that the adapted PTR model is associated with reduction in child problem behavior and increases in alternative behavior. This study expanded the current research on the PTR model and extended its use to a novel setting and population so that a standardized model for positive behavior support implementation can be developed in the family context.

Thin films that are functionally gradient improve the mechanical properties of film-substrate layered materials. Mechanical properties of such materials are found by using indentation tests. In this study, finite element models are developed to simulate the indentation test. The models are based on an axisymmetric half space of a specimen subjected to spherical indentation. The film layer through the thickness is modeled to have either homogeneous material properties or nonhomogeneous material properties that vary linearly. Maximum indenter displacement, and maximum normal and shear stresses at the interface are compared between the homogeneous model and the nonhomogeneous model for pragmatic contact length to film thickness ratios of 0.2 to 0.4, and film to substrate moduli ratios of 1 to 200 to 1. Additionally, a coefficient is derived from regression of the stress data produced by these models and compared to that used to define the pressure field in the axisymmetric Hertzian contact model. The results of this study suggest that a displacement boundary condition to an indenter produces the same results as a pressure distribution boundary condition. The critical normal stresses that occur between modeling a film as a nonhomogeneous and as a homogeneous material vary from 19% for a modulus ratio of 2.5:1 to as high as 66% for a modulus ratio of 200:1 indicating that the modeling techniques produced very different maximum normal stresses. The difference in the maximum shear stress between the nonhomogeneous and the homogeneous models varied from 19% for a 2.5:1 modulus ratio to 57% for the 200:1 modulus ratio but reached values as low as 6% for the 50:1 modulus ratio. The maximum contact depth between the nonhomogeneous and the homogeneous models varied from 14% for the 2.5:1 case to as much as 75% in the 200:1 case. The results from the reapplication of the pressure field derived from the regression coefficients and the R2 values from these regression models indicate the correctness of the regression model used as well as its ability to replicate the normal stresses in the contact area and maximum indenter displacements in a FEA model for both the homogeneous and the nonhomogeneous models for modulus ratios ranging from 2.5:1 to 200:1. The agreement between the regression based coefficients and the force based coefficients suggests the validity for the use of the theoretical axisymmetric Hertzian contact model for defining the pressure field in the contact area and displacements for both the homogeneous case and the nonhomogeneous case for the considered film to substrate moduli ratios and contact length to film thickness ratios.