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Many engineering applications make use of fiber assemblies under compression. Unfortunately, this compression behavior is difficult to predict, due to nonlinear compliance, hysteresis, and anelasticity. The main objective of this research is to develop an algorithm which is capable of incorporating the microscale features of the fiber network into macroscopic scale applications, particularly the modeling of contact mechanics in multibody systems. In micromechanical approaches, the response of a fiber assembly to an external force is related to the response of basic fiber units as well as the interactions between these units, i.e. the mechanical properties of the constituent fibers and the architecture of the assembly will both have a significant influence on the overall response of the assembly to compressive load schemes. Probabilistic and statistical principles are used to construct the structure of the uniformly-distributed random network. Different micromechanical approaches in modeling felt, as a nonwoven fiber assembly with unique mechanical properties, are explored to gain insight into the key mechanisms that influence its compressive response. Based on the deformation processes and techniques in estimating the number of fiber contacts, three micromechanical models are introduced: (1) constitutive equations for micromechanics of three-dimensional fiberwebs under small strains, in which elongation of the fibers is the key deformation mechanism, adapted for large deformation ranges; (2) micromechanical model based on the rate theory of granular media, in which bending and torsion of fibers are the predominant elemental deformations used to calculate compliances of a particular contact; and (3) a mechanistic model developed using the general deformation theory of the fiber networks with fiber bending at the micro level and a binomial distribution of fiber contacts. A well-established mechanistic model, based on fiber-to-fiber friction at the micro level, is presented for predicting the hysteresis in compression behavior of wool fiberwebs. A novel algorithm is introduced to incorporate a hysteretic micromechanical model - a combination of the mechanistic model with microstructural fiber bending, which uses a binomial distribution of the number of fiber-to-fiber contacts, and the friction-based hysteresis idea - into the contact mechanics of multibody simulations with felt-lined interacting bodies. Considering the realistic case in which a portion of fibers slides, the fiber network can be treated as two subnetworks: one from the fibers with non-sliding contact points, responsible for the elastic response of the network, and the other consisting of fibers that slide, generating irreversible hysteresis phenomenon in the fiberweb compression. A parameter identification is performed to minimize the error between the micromechanical model and the elastic part of the loading-unloading experimental data for felt, then contribution of friction was added to the obtained mechanistic compression-recovery curves. The theoretical framework for constructing a mechanistic multibody dynamic model of a vertical piano action is developed, and its general validity is established using a prototype model. Dynamic equations of motion are derived symbolically for the piano action using a graph-theoretic formulation. The model fidelity is increased by including hammer-string interaction, backcheck wire and hammer shank flexibility, a sophisticated key pivot model, nonlinear models of bridle strap and butt spring, and a novel mathematical contact model. The developed nonlinear hysteretic micromechanical model is used for the hammer-string interaction to affirm the reliability and applicability of the model in general multibody dynamic simulations. In addition, dynamic modeling of a flexible hub-beam system with an eccentric tip mass including nonlinear hysteretic contact is studied. The model represents the mechanical finger of an actuator for a piano key. Achieving a desired finger-key contact force profile that replicates that of a real pianist's finger requires dynamic and vibration analysis of the actuator device. The governing differential equations for the dynamic behavior of the system are derived using Euler-Bernoulli beam theory along with Lagrange's method. To discretize the distributed parameter flexible beam in the model, the finite element method is utilized. Excessive vibration due to the arm flexibility and also the rigid-body oscillations of the arm, especially during the period of key-felt contact, is eliminated utilizing a simple grounded rotational dashpot and a grounded rotational dashpot with a one-sided relation. The effect on vibration behavior attributed to these additional components is demonstrated using the simulated model.

The conventional route of materials development typically involves fabrication of numerous batches of specimens having a range of different microstructures generated via variations of process parameters and measurements of relevant properties of these microstructures to identify the combination of processing conditions that yield the material having desired properties. Clearly, such a trial and error based materials development methodology is expensive, time consuming, and inefficient. Consequently, it is of interest to explore alternate strategies that can lead to a decrease in the cost and time required for development of advanced materials such as composites. Availability of powerful and inexpensive computational power and progress in computational materials science permits advancement of modeling and simulations assisted materials design methodology that may require fewer experiments, and therefore, lower cost and time for materials development. The key facets of such a technology would be computational tools for (i) creating models to generate computer simulated realistic microstructures; (ii) capturing the process-microstructure relationship using these models; and (iii) implementation of simulated microstructures in the computational models for materials behavior. Therefore, development of a general and flexible methodology for simulations of realistic microstructures is crucial for the development of simulations based materials design and development technology. Accordingly, this research concerns development of such a methodology for simulations of realistic microstructures based on experimental quantitative stereological data on few microstructures that can capture relevant details of microstructural geometry (including spatial clustering and second phase particle orientations) and its variations with process parameters in terms of a set of simulation parameters. The interpolation and extrapolation of the simulation parameters can then permit generation of atlas of virtual microstructures that covers the complete range of variations of processing conditions of interest. These simulated and virtual microstructures can then be used in the micromechanical models such as FEM to analyze their constitutive properties

The primary focus of this research is to investigate the non-linear behavior of single crystal and polycrystalline relaxor ferroelectric PMN-xPT and PZN-xPT through experimentation and modeling. Characterization of single crystal and polycrystalline specimens with similar compositions was performed. These data give experimental insight into the differences that may arise in a polycrystal due to local interaction with inhomogeneities. Single crystal specimens were characterized with a novel experimental technique that reduced clamping effects at the boundary and gave repeatable results. The measured experimental data was used in conjunction with electromechanical characterizations of other compositions of single crystal specimens with the same crystallographic orientation to study the compositional effects on material properties and phase transition behavior. Experimental characterization provided the basis for the development of a model of the continuous phase transformation behavior seen in PMN-xPT single crystals. In the modeling it is assumed that a spatial chemical and structural heterogeneity is primarily responsible for the gradual phase transformation behavior observed in relaxor ferroelectric materials. The results are used to simulate the effects of combined electrical and mechanical loading. An improved rate-independent micromechanical constitutive model based on the experimental observations of single crystal and polycrystalline specimens under large field loading is also presented. This model accounts for the non-linear evolution of variant volume fractions. The micromechanical model was calibrated using single crystal data. Simulations of the electromechanical behavior of polycrystalline ferroelectric materials are presented. These results illustrate the effects of non-linear single crystal behavior on the macroscopic constitutive behavior of polycrystals.

The present work investigates the effect of carbon nanotube (CNT) inclusions on the electrical and thermal conductivity of a thermoset epoxy resin. The characterization of electrical and thermal conductivity of CNT/epoxy composites is presented. Pristine, oxidized, and fluorine-functionalized unpurified CNT mixtures ("XD grade") were dispersed in an epoxy matrix, and the effect of stirring rate and pre-curing of the epoxy on the dispersion of the CNTs was evaluated. In order to characterize the dispersion of the CNTs at different length scales, Optical Microscopy (OM), Raman Spectroscopy, and Scanning Electron Microscopy (SEM) was performed. Samples of varying CNT weight fractions were fabricated in order to find the effect of CNT weight fraction on thermal and electrical conductivity. Electrical conductivity was measured using a dielectric spectrometer, and thermal conductivity was determined by a transient plane source thermal analyzer. It was found that electrical conductivity increases by orders of magnitude for the pristine and oxidized XD CNT composites relative to the neat epoxy matrix, while fluorinated XD CNT composites remain electrically non-conductive. A small, but significant, increase in thermal conductivity was observed for pristine, oxidized, and fluorinated XD CNT composites, showing a linear increase in thermal conductivity with increasing CNT weight fraction. Pristine XD CNTs were ball-milled for different times in order to reduce the degree of agglomeration and entanglement of CNTs, and composites were fabricated using the same technique as with non-milled XD CNTs. Using ball-milled CNTs shows improved dispersion but results in an electrically non-conductive composite at the CNT weight fractions tested. The thermal conductivity of the ball-milled CNT samples shows an initial increase higher than that of non-milled pristine, oxidized, and fluorinated XD CNTs, but remains constant with increasing CNT weight fraction. A micromechanics model based on the composite cylinders method was implemented to model the electrical and thermal conductivity of the CNT/epoxy composites. Nanoscale effects in electrical and thermal conduction, such as electron hopping and interface thermal resistance, respectively, were incorporated into the model in order to accurately predict the acquired results. Modeling results show good agreement with acquired experimental results.

abstract: Advanced composites are being widely used in aerospace applications due to their high stiffness, strength and energy absorption capabilities. However, the assurance of structural reliability is a critical issue because a damage event will compromise the integrity of composite structures and lead to ultimate failure. In this dissertation a novel homogenization based multiscale modeling framework using semi-analytical micromechanics is presented to simulate the response of textile composites. The novelty of this approach lies in the three scale homogenization/localization framework bridging between the constituent (micro), the fiber tow scale (meso), weave scale (macro), and the global response. The multiscale framework, named Multiscale Generalized Method of Cells (MSGMC), continuously bridges between the micro to the global scale as opposed to approaches that are top-down and bottom-up. This framework is fully generalized and capable of modeling several different weave and braids without reformulation. Particular emphasis in this dissertation is placed on modeling the nonlinearity and failure of both polymer matrix and ceramic matrix composites. / Dissertation/Thesis / Ph.D. Aerospace Engineering 2011

This study concerns four high performance structural alloys designed to withstand the extreme temperature and irradiation environment inside fusion and fission fast breeder reactors: two Reduced Activation Ferritic Martensitic (RAFM) steels (Fe-14wt%Cr and a European standard alloy EUROFER97) and two equivalent Oxide Dispersion Strengthened (ODS) steels (Fe-14wt%Cr ODS (CEA ODS) and EUROFER ODS). Neutron irradiation of the samples was impractical due to timescale and specific handling requirements for radioactive samples. Instead, ion implantation was used to simulate the helium and damage of neutron irradiation. Samples of each alloy were subjected to a range of ion implantations: 75appm He, 2000appm He, 2000appm He + 4.5dpa Fe and 2000appm Ne. The matrix of four materials and five implantation conditions was analysed using the following experimental techniques: nanohardness indentation, Vickers hardness testing, micropillar compression, microcantilever bending, transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDX). These techniques were used to compare the properties of the unimplanted materials and their response to implantation. Yield stress (σ_y) was comparable across hardness testing and microcantilever bending, and consistently showed σ_y Fe-14wt%Cr < EUROFER < EUROFER ODS < CEA ODS. When subject to helium implantation, 75appm He caused insignificant changes in σy while 2000appm He increased σ_y in all materials. This increase was most significant in Fe-14wt%Cr due to its low grain boundary density and lack of oxide/carbide particles. The particle dispersions in the other materials act as helium traps, preventing the formation of TEM visible bubbles and reducing the hardening effects of the helium. Across all results it becomes clear that, although not to the degree of the ODS materials, EUROFER is more radiation resistant than Fe-14wt%Cr. It therefore appears that it is the presence of a complex microstructure including small grains and a distribution of oxide or carbide particles, rather than the specific inclusion of oxide nanoparticles, that provides RAFM steels with superior irradiation resistance properties.

Os meios rochosos são compostos por blocos de rochas intactos e por descontinuidades. As descontinuidades representam zonas de baixa rigidez, onde as propriedades do maciço estão degradadas, reduzindo a resistência do mesmo. Elas também constituem caminhos para o fluxo de fluidos no interior da rocha. O estudo do comportamento hidráulico-mecânico acoplado existente nos meios porosos é realizado pela poroelasticidade, que relaciona os campos de tensões e deformações no maciço, gerados pela deformação mecânica do esqueleto e pela ação do fluido pressurizado nos poros. Uma abordagem micromecânica permite estender os resultados clássicos da teoria de poroelasticidade para o caso de juntas que são capazes de transferir esforços ao longo de suas faces. Neste contexto, o meio rochoso heterogêneo é substituído por um meio homogêneo equivalente, pela aplicação do conceito de mudança de escala da teoria da homogeneização, que possibilita a determinação das propriedades efetivas do maciço. Demonstra-se que, para certas distribuições geométricas das juntas, é possível obter soluções analíticas para o comportamento do maciço pela aplicação de estimativas como, por exemplo, o esquema Mori-Tanaka, onde as juntas são modeladas como esferoides. Um modelo numérico via método dos elementos finitos, que considera explicitamente as juntas, é usado para comparar os resultados obtidos. / Rock media are composed by blocks of intact rock and discontinuities. Discontinuities represent zones of low stiffness, where the mass properties of the rock are degraded, with reduced resistance. They also provide ways for fluid flow within the rock. The study of coupled mechanical-hydraulic behavior existing in porous media is perfomed by poroelasticity, which relates the stress and strain fields in a rock mass generated by the mechanical deformation of the skeleton and the action of pressurized fluid in the pores. A Micromechanics approach allows to extend the classical results of the theory of poroelasticity to the case of joints that are able to transfer stresses along their faces. In this context, a heterogeneous rock media is replaced by an equivalent homogeneous medium by applying the micro-macro approach from the theory of homogenization, which allows the determination of the effective properties of the rock mass. It is shown that, for some geometric distributions of the joints, it is possible to obtain analytical solutions for the rock behavior by applying estimates methods as the Mori-Tanaka scheme, where the joints are modeled as oblong spheroids. A numerical model via the finite element method, where the joints are considering explicitly, is used in order to compare the results.

Os meios rochosos são compostos por blocos de rochas intactos e por descontinuidades. As descontinuidades representam zonas de baixa rigidez, onde as propriedades do maciço estão degradadas, reduzindo a resistência do mesmo. Elas também constituem caminhos para o fluxo de fluidos no interior da rocha. O estudo do comportamento hidráulico-mecânico acoplado existente nos meios porosos é realizado pela poroelasticidade, que relaciona os campos de tensões e deformações no maciço, gerados pela deformação mecânica do esqueleto e pela ação do fluido pressurizado nos poros. Uma abordagem micromecânica permite estender os resultados clássicos da teoria de poroelasticidade para o caso de juntas que são capazes de transferir esforços ao longo de suas faces. Neste contexto, o meio rochoso heterogêneo é substituído por um meio homogêneo equivalente, pela aplicação do conceito de mudança de escala da teoria da homogeneização, que possibilita a determinação das propriedades efetivas do maciço. Demonstra-se que, para certas distribuições geométricas das juntas, é possível obter soluções analíticas para o comportamento do maciço pela aplicação de estimativas como, por exemplo, o esquema Mori-Tanaka, onde as juntas são modeladas como esferoides. Um modelo numérico via método dos elementos finitos, que considera explicitamente as juntas, é usado para comparar os resultados obtidos. / Rock media are composed by blocks of intact rock and discontinuities. Discontinuities represent zones of low stiffness, where the mass properties of the rock are degraded, with reduced resistance. They also provide ways for fluid flow within the rock. The study of coupled mechanical-hydraulic behavior existing in porous media is perfomed by poroelasticity, which relates the stress and strain fields in a rock mass generated by the mechanical deformation of the skeleton and the action of pressurized fluid in the pores. A Micromechanics approach allows to extend the classical results of the theory of poroelasticity to the case of joints that are able to transfer stresses along their faces. In this context, a heterogeneous rock media is replaced by an equivalent homogeneous medium by applying the micro-macro approach from the theory of homogenization, which allows the determination of the effective properties of the rock mass. It is shown that, for some geometric distributions of the joints, it is possible to obtain analytical solutions for the rock behavior by applying estimates methods as the Mori-Tanaka scheme, where the joints are modeled as oblong spheroids. A numerical model via the finite element method, where the joints are considering explicitly, is used in order to compare the results.