The objective of the present study was to develop a fluid flow-coupled distinct element model capable of capturing the undrained behaviour of granular soils by considering fundamental physical mechanisms that involve fluid flow and particle interaction. The method considers granular media as assemblies of ellipsoidal particles arranged on a plane and interacting by means of contact forces. Saturation effects are incorporated by assuming that particles are immersed in fluid, the flow of which is simulated as occurring through a network of conduits. The flow through conduits is according to a Hagen-Poiseuille relation; a transient solution is obtained by solving a system of differential equations. The developed fluid-flow coupled distinct element was used to conduct various numerical simulations and the mechanisms of undrained deformations were examined from a micromechanical point of view. The dissertation begins with a literature review on the undrained behaviour of granular materials as observed in laboratory experiments. A review of previous attempts to simulate undrained tests micromechanically is also presented, and the advantages and disadvantages of various methods are examined. The capability of the developed model to simulate two-dimensional fluid-flow and pressure dissipation problems is demonstrated by means of comparisons with analytical solutions. Fluid pressure dissipation problems are qualitatively compared with Terzaghi's one-dimension theory of consolidation. It is shown that transient flow problems are accurately modelled by the fluid flow network approach. Simulated compression tests were carried out to examine the effects of different confining pressures and initial densities on the macroscopic response. The results compare favorably with those commonly observed in undrained laboratory experiments. Simulated tests are analyzed from a micromechanical point of view. It is shown that macroscopic behaviour can be traced to changes in micromechanical fabric descriptors. The effects of the interparticle friction angle on the undrained behaviour of the assemblies are investigated. The undrained strength is considerably increased by increasing interparticle friction. The main mechanism found to be responsible for the development of higher strength is the tendency of the specimens to dilate during shear distortion. The effects of the principal stress direction on the macroscopic response are examined. The behaviour of initially anisotropic samples is significantly altered by the direction of the principal stresses relative to the anisotropy direction. It is demonstrated that macroscopic permeability of the media has a considerable effect on the strength. This behaviour is attributed to the inhomogeneity of pore pressure distributions which increases with decreased permeability. The results presented are generally in agreement with observations previously reported from laboratory experiments. The possible applications of the model for future research are also discussed.

The objective of the present study was to develop a fluid flow-coupled distinct element model capable of capturing the undrained behaviour of granular soils by considering fundamental physical mechanisms that involve fluid flow and particle interaction. The method considers granular media as assemblies of ellipsoidal particles arranged on a plane and interacting by means of contact forces. Saturation effects are incorporated by assuming that particles are immersed in fluid, the flow of which is simulated as occurring through a network of conduits. The flow through conduits is according to a Hagen-Poiseuille relation; a transient solution is obtained by solving a system of differential equations. The developed fluid-flow coupled distinct element was used to conduct various numerical simulations and the mechanisms of undrained deformations were examined from a micromechanical point of view. The dissertation begins with a literature review on the undrained behaviour of granular materials as observed in laboratory experiments. A review of previous attempts to simulate undrained tests micromechanically is also presented, and the advantages and disadvantages of various methods are examined. The capability of the developed model to simulate two-dimensional fluid-flow and pressure dissipation problems is demonstrated by means of comparisons with analytical solutions. Fluid pressure dissipation problems are qualitatively compared with Terzaghi's one-dimension theory of consolidation. It is shown that transient flow problems are accurately modelled by the fluid flow network approach. Simulated compression tests were carried out to examine the effects of different confining pressures and initial densities on the macroscopic response. The results compare favorably with those commonly observed in undrained laboratory experiments. Simulated tests are analyzed from a micromechanical point of view. It is shown that macroscopic behaviour can be traced to changes in micromechanical fabric descriptors. The effects of the interparticle friction angle on the undrained behaviour of the assemblies are investigated. The undrained strength is considerably increased by increasing interparticle friction. The main mechanism found to be responsible for the development of higher strength is the tendency of the specimens to dilate during shear distortion. The effects of the principal stress direction on the macroscopic response are examined. The behaviour of initially anisotropic samples is significantly altered by the direction of the principal stresses relative to the anisotropy direction. It is demonstrated that macroscopic permeability of the media has a considerable effect on the strength. This behaviour is attributed to the inhomogeneity of pore pressure distributions which increases with decreased permeability. The results presented are generally in agreement with observations previously reported from laboratory experiments. The possible applications of the model for future research are also discussed.

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.

In recent impact and penetration mechanical tests, steel projectiles (AISI4340) were impacted into targets like concrete with striking velocities (1200 m/s to 1500 m/s). Results indicated a material removal from the nose of the projectile, phase changes of the projectile materials, a reduction in the length of the projectile, and a blunting of the nose shape. These observations cannot be explained by current theories and numerical integration code that are used to study impact and penetration mechanics. Thus, the objectives of the thesis research are to (a) formulate and characterize the mechanisms responsible for the material erosion of the impacting projectile and the mass loss from the nose region; and (b) to determine the physical properties of alloy steels that are important to penetration mechanics from ab initio methods. The results can be used to design new projectile materials that can provide the desired penetration characteristics. These objectives are accomplished by investigating two related problems. The first problem is to formulate simplified models that can explain the penetration mechanics. The new models include the varying cross-section nose, changes of yield stress behind the shock wave and high strain rate phase transitions. Nose erosion effects, and time-dependent penetration path can be determined by integrating ODEs. A cavity expansion theory model is used to obtain the target resistance that is responsible slowing and deforming the penetrating projectile. The second problem concerns the determination of the constitutive relations from ab initio methods. The equation of state (EOS) and magnetic moments for alloy steels are investigated by using a special quasirandom structure technique and ab initio methods. Specifically, EOS for an interstitial disordered alloy Fe1-x-yNixCy is developed. First, the EOS of iron and phase transition of iron are studied and validated. Second, Nickel is considered to investigate the substitutional disordered alloy Fe1-x-yNixCy. Third, Carbon is placed at an interstitial position in the substitutional disordered alloy. These investigations will form foundation for future work involving new projectile with steel nose and shank made of multifunctional structural energetic materials.

This thesis focuses on the micromechanical modeling of particulate viscoelastic composite materials in the quasi-static frequency domain to approximate macroscopic damping behavior and has two main objectives. The first objective is the development of a robust frequency dependent multiscale model. For this purpose, the self-consistent (SC) mean-field micromechanical model introduced by Cherkaoui et al [J. Eng. Mater. Technol. 116, 274-278 (1994)] is extended to include frequency dependence via the viscoelastic correspondence principal. The quasi-static model is then generalized using dilute strain concentration tensor formulation and validated by comparison with complex bounds from literature, acoustic and static experimental data, and established models. The second objective is SC model implementation as a tool for the design of high loss materials. This objective is met by integrating the SC model into a Compromise Decision Support Protocol (CDSP) to explore the microstructural design space of an automobile windshield. The integrated SC-CDSP design space exploration results definitively indicate that one microstructural variable dominates structure level acoustic isolation and rigidity: negative stiffness. The work concludes with a detailed description of the fundamental mechanisms leading to negative stiffness behavior and proposes two negative stiffness inclusion designs.

The overall goal of the present research is to provide a computationally based methodology to realize the projected extraordinary properties of Carbon Nanotube (CNT)- reinforced composites and polymeric nanofibers for engineering applications. The discovery of carbon nanotubes (CNT) and its derivatives has led to considerable study both experimentally and computationally as carbon based materials are ideally suited for molecular level building blocks for nanoscale systems. Research in nanomechanics is currently focused on the utilization of CNTs as reinforcements in polymer matrices as CNTs have a very high modulus and are extremely light weight. The nanometer dimension of a CNT and its interaction with a polymer chain requires a study involving the coupling of the length scales. This length scale coupling requires analysis in the molecular and higher order levels. The atomistic interactions of the nanotube are studied using molecular dynamic simulations. The elastic properties of neat nanotube as well as doped nanotube are estimated first. The stability of the nanotube under various conditions is also dealt with in this dissertation. The changes in the elastic stiffness of a nanotube when it is embedded in a composite system are also considered. This type of a study is very unique as it gives information on the effect of surrounding materials on the core nanotube. Various configurations of nanotubes and nanocomposites are analyzed in this dissertation. Polymeric nanofibers are an important component in tissue engineering; however, these nanofibers are found to have a complex internal structure. A computational strategy is developed for the first time in this work, where a combined multiscale approach for the estimation of the elastic properties of nanofibers was carried out. This was achieved by using information from the molecular simulations, micromechanical analysis, and subsequently the continuum chain model, which was developed for rope systems. The continuum chain model is modified using properties of the constituent materials in the mesoscale. The results are found to show excellent correlation with experimental measurements. Finally, the entire atomistic to mesoscale analysis was coupled into the macroscale by mathematical homogenization techniques. Two-scale mathematical homogenization, called asymptotic expansion homogenization (AEH), was used for the estimation of the overall effective properties of the systems being analyzed. This work is unique for the formulation of spectral/hp based higher-order finite element methods with AEH. Various nanocomposite and nanofibrous structures are analyzed using this formulation. In summary, in this dissertation the mechanical characteristics of nanotube based composite systems and polymeric nanofibrous systems are analyzed by a seamless integration of processes at different scales.

Polymer nanocomposites refer to a broad range of composite materials with polymer acting as the matrix and any material which has at least one dimension in the order of 1 ~ 100 nanometer acting as the filler. Due to unprecedented improvement observed in properties of the nanocomposites, research interest in this area has grown exponentially in recent years. In designing better nano-composites for advanced technological applications some of the major challenges are: understanding the structure-property relationships, interaction and integrity of the two components at the interface, the role of nanofillers in enhancing the properties of the resulting material. In our work, we have utilized first principle calculations, atomistic simulations, coarse-grained modeling and constitutive equations to develop structureproperty relationships for an amorphous aromatic piezoelectric polyimide substituted with nitrile dipole, carbon nanotubes and resulting nanocomposites. We have studied in detail structure-property relationships for carbon nanotubes and (? ?CN)APB/ODPA polyimide. We have developed chemically sound coarse-grained model based on atomic level simulations of the piezoelectric polyimide to address the larger length and time scale phenomena. The challenge of coarse grain model for these polymers is to reproduce electrical properties in addition to the structure and energetics; our model is the first to successfully achieve this goal. We have compared and analyzed atomistic scale simulation results on the nanocomposite with those predicted from micromechanics analysis. Notably, we have investigated the time dependent response of these highly complex polymers, to our best knowledge this is the first of its kind. In particular we have studied the thermal, mechanical and dielectric properties of the polyimide, nanotube and their nanocomposites through multi-scale modeling technique. We expect the results obtained and understanding gained through modeling and simulations may be used in guiding development of new nanocomposites for various advanced future applications. In conclusion we have developed a computational paradigm to rationally develop next generation nano-materials.

Eshelby-type inclusion problems of an infinite or a finite homogeneous isotropic elastic body containing an arbitrary-shape inclusion prescribed with an eigenstrain and an eigenstrain gradient are analytically solved. The solutions are based on a simplified strain gradient elasticity theory (SSGET) that includes one material length scale parameter in addition to two classical elastic constants. For the infinite-domain inclusion problem, the Eshelby tensor is derived in a general form by using the Green’s function in the SSGET. This Eshelby tensor captures the inclusion size effect and recovers the classical Eshelby tensor when the strain gradient effect is ignored. By applying the general form, the explicit expressions of the Eshelby tensor for the special cases of a spherical inclusion, a cylindrical inclusion of infinite length and an ellipsoidal inclusion are obtained. Also, the volume average of the new Eshelby tensor over the inclusion in each case is analytically derived. It is quantitatively shown that the new Eshelby tensor and its average can explain the inclusion size effect, unlike its counterpart based on classical elasticity. To solve the finite-domain inclusion problem, an extended Betti’s reciprocal theorem and an extended Somigliana’s identity based on the SSGET are proposed and utilized. The solution for the disturbed displacement field incorporates the boundary effect and recovers that for the infinite-domain inclusion problem. The problem of a spherical inclusion embedded concentrically in a finite spherical body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. It is demonstrated through numerical results that the newly obtained Eshelby tensor can capture the inclusion size and boundary effects, unlike existing ones. Finally, a homogenization method is developed to predict the effective elastic properties of a heterogeneous material using the SSGET. An effective elastic stiffness tensor is analytically derived for the heterogeneous material by applying the Mori-Tanaka and Eshelby’s equivalent inclusion methods. This tensor depends on the inhomogeneity size, unlike what is predicted by existing homogenization methods based on classical elasticity. Numerical results for a two-phase composite reveal that the composite becomes stiffer when the inhomogeneities get smaller.

Despite efforts by clinicians and scientists world-wide, coronary artery disease remains to be the leading cause of morbidity and mortality in industrialized nations. Development of a tissue engineered coronary by-pass graft with low thrombogenicity and immune responses, suitable mechanical properties, and a capacity to remodel to their environment could have a significant impact on the treatment of coronary artery disease. While many methods for the tissue engineering of blood vessels have been developed, one promising approach is the self-assembly method. Using autologous cells that produce an endogenous extracellular matrix (ECM), the potential for therapeutic success is high due to biocompatibility. However, despite these advantages, improvements can be made which will give the grafts an even higher rate of patency. This dissertation presents a study of the characterization of the biaxial mechanical properties of self-assembly tissue engineered blood vessels (SA-TEBV), as well as developing a framework for fabrication strategies of SA-TEBV. Native arteries are exposed to multiaxial mechanical loads, including (a pulsatile) blood pressure that causes the vessel to cyclically distend circumferentially, blood flow that induces a shearing load along the luminal surface, and an axial extending load; the latter is relieved upon excision, causing the vessel to retract. These mechanical loads introduce intramural wall stresses and flow induced wall shear stresses that play a key role in mechano-biological signaling and tissue homeostasis. Until now, the mechanical properties of SA-TEBV have only been characterized in the circumferential direction (i.e. burst pressure and circumferential elastic modulus). The objective of this work is to characterize the biaxial mechanical properties of SA-TEBV to quantify their mechanical behavior and local intramural stresses under physiological loading. The work will show that while the global mechanical response of the SA-TEBV is similar to that of native arteries (and potentially sufficient), the local intramural stresses (using the current fabrication techniques) differ greatly from native coronary arteries. Therefore, a novel approach to fabricate the self-assembly derived tissue sheets is developed and tested which utilizes biaxial mechanical stimulation to alter the microstructure, thereby controlling their mechanical response.

Estimating the in situ mechanical properties of sediments containing gas hydrates from seismic or log data is essential for evaluating the risks posed by mechanical failure during drilling, completions, and producing operations. In this paper, a method is presented for constructing correlations between the mechanical properties of gas hydrate bearing sediments and geophysical data. A theory based on micromechanics models was used to guide the selection of parameters that govern the physical behavior of sediments. A set of nondimensionalized relations between elastoplastic properties and those that could be inferred from log or seismic data was derived. Using these relations, a correlation for the Young’s modulus was constructed for sands with methane and THF hydrate using data from a wide variety of sources. It was observed that the correlation did not fit data obtained from samples with high THF hydrate saturations, due possibly to the existence of cohesive mechanisms that operate in such regimes.