Epithelial tissues, one of the four primary tissue structures found in our human body, are known to comprise of tiny cells interconnected in a unique continuous pattern. In most cases, they serve a dual purpose of protecting the internal organs from physical damage, and at the same time, enable in facilitating inter-cellular activities and prevent pathogen break ins. While the tissue mechanics and its proliferation have been scrutinized to great detail, it is their geometric uniqueness, that has remained more or less unexplored. With an intent of doing the same, this thesis identifies and explores those geometric properties/parameters that have an influence on the micro structure’s homogenized and localized response. However, it does so by extracting the microstructures profile and representing its cell edges via three dimensional beam elements - hence the name, bio-inspired structures. The analysis is carried out by first developing a staggered Representative Volume Element (RVE)using finite elements, and identifying its appropriate size. The staggered assembly aids in minimizing boundary effects from creeping in, and at the same time, provides the requisite statistical homogeneity. This is followed by the geometry study. A wide range of epithelial geometries are considered for the study, ranging from completely isotropic skin models, to in plane anisotropic cuboidal structures and out of plane anisotropic stratified geometries. The effects of orientation, relative density and edge length are extracted and studied in great detail. It is observed that cell edges initial orientation has a direct dependence on the particle distribution, whereas the change in orientation is largely dependent on the deformation the microstructure is subjected to. Relative density is documented to show a direct correlation to a materials homogenized response i.e. larger the relative density, greater is the microstructures stiffness and homogenized stress response to the same deformation. Edge length, on the other hand is observed to showcase a downward trend on the cell edge’s axial stress. On average, in any kind of distribution and any kind of deformation, smaller cell edges are known to showcase larger stresses, as compared to the larger cell edges.

<p>Injection to the subcutaneous (SC) tissue is one of the preferred methods for drug delivery of pharmaceuticals, from small molecules to monoclonal antibodies. Delivery to SC has become widely popular in part thanks to the low cost, ease of use, and effectiveness of drug delivery through the use of auto-injector devices. However, injection physiology, from initial plume formation to the eventual uptake of the drug in the lymphatics, is highly dependent on SC mechanics, poroelastic properties in particular. Yet, the poroelastic properties of SC have been understudied. In this thesis, I present a two-pronged approach to understanding the poroelastic properties of SC. Experimentally, mechanical and fluid transport properties of SC were measured with confined compression experiments and compared against gelatin hydrogels used as SC-phantoms. It was found that SC tissue is a highly non-linear material that has viscoelastic and porohyperelastic dissipation mechanisms. Gelatin hydrogels showed a similar, albeit more linear response, suggesting a micromechanical mechanism may underline the nonlinear behavior. The second part of the thesis focuses on the multiscale modeling of SC to gain a fundamental understanding of how geometry and material properties of the microstructure drive the macroscale response. SC is composed of adipocytes (fat cells) embedded in a collagen network. The geometry can be characterized with Voroni-like tessellations. Adipocytes are fluid-packed, highly deformable and capable of volume change through fluid transport. Collagen is highly nonlinear and nearly incompressible. Representative volume element (RVE) simulations with different Voroni tesselations shows that the different materials, coupled with the geometry of the packing, can contribute to different material response under the different kinds of loading. Further investigation of the effect of geometry showed that cell packing density nonlinearly contributes to the macroscale response. The RVE models can be homogenized to obtain macroscale models useful in large scale finite element simulations of injection physiology. Two types of homogenization were explored: fitting to analytical constitutive models, namely the Blatz-Ko material model, or use of Gaussian process surrogates, a data-driven non-parametric approach to interpolate the macroscale response.</p>

<p>The superior high-temperature elastic-plastic properties coupled with greater damage tolerance when compared with monolithic ceramics make ceramic matrix composites, CMCs, promising candidates for challenging applications such as engine components, rocket nozzles, cutting tools and nuclear energy reactor core components. Anelastic recovery is the time-dependent back strain observed upon the load removal following creep. In whisker-reinforced CMCs this can be a factor limiting operating conditions. Plastic strain misfit between two phases is thought to be the main driver in terms of the interactions within a percolating network. However, the network deformation mechanisms are still unclear and a previous neutron diffraction study showed an unexpected decrease of peak width after creep contradicting the theoretical predictions.</p> <p>In this contribution, the finite element method (FEM) is applied to a representative volume element (RVE) with proper boundary conditions in order to simulate the creep deformation and hot pressing processes. Three geometries have been generated and studied: a 3D randomly-oriented short-fiber unit cell without fiber to fiber contact, generated by a random sequential adsorption algorithm; 3D regularly aligned single fiber unit cells; and 2D regularly aligned percolating unit cells. Deformation mechanism has been studied from an energy point of view and compared with a modified analytical model. Then a virtual diffraction model has been developed providing a framework to transfer information between the FEM simulations (strain fields) and the diffraction pattern in terms of the peak width (full width at half maximum: <strong><em>FWHM</em></strong>) and peak position as a measure of stress distribution and mean stress state respectively. Furthermore, the coupling effects of external stress, deformation mode, and thermal stress on the diffraction patterns have been studied.</p> <p>The critical importance of a percolating whisker network for the anelastic recovery is demonstrated based on the 3D multi-whisker random unit cell. Whisker bending is shown to be the dominant mechanism over contact effects during the creep deformation of a composite containing a well aligned percolating whisker network based on the 2D unit cell model. Good qualitative agreement was found between our FEM simulations and the analytical model of Wilkinson and Pompe with regards to the maximum recoverable strain and the characteristic relaxation time. The analytical model captures all the critical factors characterizing the strain recovery, e.g., the effect of creep pre-exponent constant, whisker Young’s modulus and aspect ratio. Furthermore, it is found that the deformation from an initial stress-free state inevitably introduces peak broadening of whiskers inside the matrix. Several factors determine the peak-width and -shift, i.e., creep strain, applied stress, aspect ratio and geometry. However, thermal stress from the cooling stages following creep and hot pressing processes shelters this broadening effect and complicates the trends. Wide-ranging peak-width changes from narrowing to broadening are predicted depending on the geometry and applied stress. The peak position is shifted to a lower angle due to this thermal effect. This clearly explains the contradicting phenomena motivating this work and leads to that recommendation that a diffraction source with high angular resolution is needed to detect the subtle change of peak profile during creep.</p> / Doctor of Philosophy (PhD)

Among the many active materials in use today, piezoelectric composite patches have enabled notable advances in emerging technologies such as disturbance sensing, control of flexible structures, and energy harvesting. The macro fiber composite (MFC), in particular, is well known for its outstanding performance. Multiscale models are typically required for smart-structure design with MFCs. This is due to the need for predicting the macroscopic response (such as tip deflection under a transverse load or applied voltage) while accounting for the fact that the MFC has microscale details. Current multiscale models of the MFC exclusively focus on predicting the macroscopic response with homogenized material properties. There are a limited number of homogenized properties available from physical experiments and various aspects of existing homogenization techniques for the MFC are shown here to be inadequate. Thus, new homogenized models of the MFC are proposed to improve smart-structure predictions and therefore improve device design. It is notable that current multiscale modeling efforts for MFCs are incomplete since, after homogenization, the local fields such as stresses and electric fields have not been recovered. Existing methods for obtaining local fields are not applicable since the electrodes of the MFC are embedded among passive layers. Therefore, another objective of this work was to find the local fields of the MFC without having the computational burden of fully modeling the microscopic features of the MFC over a macroscale area. This should enable smart-structure designs with improved reliability because failure studies of MFCs will be enabled. Large-scale 3D finite element (FE) models that included microscale features were constructed throughout this work to verify the multiscale methodologies. Note that after creating a free account on cdmhub.org, many files used to create the results in this work can be downloaded from https://cdmhub.org/projects/ernestocamarena.<br><br>First, the Mechanics of Structure Genome (MSG) was extended to provide a rigorous analytical homogenization method. The MFC was idealized to consist of a stack of homogeneous layers where some of the layers were homogenized with existing rules of mixtures. For the analytical model, the electrical behavior caused by the interdigitated electrodes (IDEs) was approximated with uniform poling and uniform electrodes. All other assumptions on the field variables were avoided; thus an exact solution for a stack of homogeneous layers was found with MSG. In doing so, it was proved that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures was developed to homogenize the entire MFC layup so as to obtain the complete set of effective device properties. Since various assumptions were avoided and since the property set is now complete, it is expected that greater energy equivalence between reality and the homogenized model has been made possible. The derivation clarified what the electrical behavior of a homogenized solid with internal electrodes should be—an issue that has not been well understood. The behavior was verified by large-scale FE models of an isolated MFC patch.<br> <br>Increased geometrical fidelity for homogenization was achieved with an FE-based RVE analysis that accounted for finite-thickness effects. The presented theory also rectifies numerous issues in the literature with the use of the periodic boundary conditions. The procedure was first developed without regard to the internal electrodes (ie a homogenization of the active layer). At this level, the boundary conditions were shown to satisfy a piezoelectric macrohomogeneity condition. The methodology was then applied to the full MFC layup, and modifications were implemented so that both types of MFC electrodes would be accounted for. The IDE case considered nonuniform poling and electric fields, but fully poled material was assumed. The inherent challenges associated with these nonuniformities are explored, and a solution is proposed. Based on the homogenization boundary conditions, a dehomogenization procedure was proposed that enables the recovery of local fields. The RVE analysis results for the effective properties revealed that the homogenization procedure yields an unsymmetric constitutive relation; which suggests that the MFC cannot be homogenized as rigorously as expected. Nonetheless, the obtained properties were verified to yield favorable results when compared to a large-scale 3D FE model.<br> <br>As a final test of the obtained effective properties, large-scale 3D FE models of MFCs acting in a static unimorph configuration were considered. The most critical case to test was the smallest MFC available. Since none of the homogenized models account for the passive MFC regions that surround the piezoelectric fiber array, some of the test models were constructed with and without the passive regions. Studying the deflection of the host substrate revealed that ignoring the passive area in smaller MFCs can overpredict the response by up to 20%. Satisfactory agreement between the homogenized models and a direct numerical simulation were obtained with a larger MFC (about a 5% difference for the tip deflection). Furthermore, the uniform polarization assumption (in the analytical model) for the IDE case was found to be inadequate. Lastly, the recovery of the local fields was found to need improvement.<br><br><br>

<p>Modern structural materials utilize tailored microstructures to retain peak performance within the most volatile operating conditions. Features such as grain size, grain boundary (GB) character and morphology and secondary phases are just a few of the tunable parameters. By tailoring these types of microstructural features, the deformation behavior of the material is also altered. The localization of plastic strain directly correlated to material failure. Thus, a systematic approach was utilized to understand the effect of microstructural features on the localization of plastic deformation utilizing digital image correlation (DIC). First, at the macroscopic scale, strain accumulation is known to form parallel to the plane of maximum shear stress. The local deviations in the deformation pathways at the meso-scale are investigated relative to the plane of maximum shear stress. The deviations in the deformation pathways are observed to be a function of the accumulated local plastic strain magnitude and the grain size. Next, strains characterized via DIC were used to calculate a value of incremental slip on the active slip systems and identify cases of slip transmission. The incremental slip was calculated based on a Taylor-Bishop-Hill algorithm, which determined a qualitative assessment of deformation on a given slip system, by satisfying compatibility and identifying the stress state by the principle of virtual work. Inter-connected slip bands, between neighboring grains, were shown to accumulate more incremental slip (and associated strain) relative to slip bands confined to a single grain, where slip transmission did not occur. These results rationalize the role of grain clusters which lead to intense strain accumulation and thus serve as potential sites for fatigue crack initiation. Lastly, at GB interfaces, the effect of GB morphology (planar or serrated) on the cavitation behavior was studied during elevated temperature dwell-fatigue at 700 °C. The resulting γ′ precipitate structures were characterized near GBs and within grains. Along serrated GBs coarsened and elongated <a>γ′ </a>precipitates formed and consequently created adjacent regions that were denuded of γ′ precipitates. Dwell-fatigue experiments were performed at low and high stress amplitudes which varied the amount of imparted strain on the specimens.<a> Additionally, the regions denuded of the γ′ precipitates were observed to localize strain and to be initial sites of cavitation.</a> <a>These results present a quantitative strain analysis between two GB morphologies, which provided the micromechanical rationale for the increased proclivity for serrated GBs to form cavities.</a></p>

The effective behavior of composite materials is of great interest in materials science. The properties of such a material at the macroscale can be directly coupled to the properties of the material at the microscale. The random distribution of microscopic phases can be simulated using models of stochastic geometry. Random, two-dimensional, two-phase microstructures were constructed by stochastic simulation using the planar Boolean model. An extensive study was conducted to relate the effective hyperelastic material behavior to the stochastic parameters of the Boolean model and the physical parameters of the microstructure. Well-known approaches to determine the size of the representative volume element were adapted for this context and their results were compared.