Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2000. / Title from document title page. Document formatted into pages; contains xiii, 183 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 180-183).

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2005. / Includes bibliographical references (p. 57-59).

Thesis (Ph.D.)--Syracuse University, 2008. / "Publication number: AAT 3345017."

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 104-107). Also available via the Internet.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 70-72). Also available via the Internet.

Theses (M.S.)--Marquette University, 2009. / John P. Borg, Jon Koch, G.E. Otto Widera, Advisors.

Multiscale analysis procedures for composites often involve coupling the macroscale (e.g., structural) and meso/microscale (e.g., ply, constituent) levels. These procedures are often computationally inefficient and thus are limited to coarse subscale discretizations. In this work, various computational strategies were employed to enhance the efficiency of multiscale analysis procedures. An ensemble averaging technique was applied to stochastic microscale simulation results based on the generalized method of cells (GMC) to assess the discretization required in multiscale models. The procedure was shown to be applicable for micromechanics analyses involving both elastic materials with damage and viscoplastic materials. A trade-off in macro/microscale discretizations was assessed. By appropriately discretizing the macro/microscale domains, similar predicted strengths were obtained at a significantly less computational cost. Further improvements in the computational efficiency were obtained by appropriately initiating multiscale analyses in a macroscale domain. A stress-based criterion was used to initiate lower length scale GMC calculations at macroscale finite element integration points without any a priori knowledge of the critical regions. Adaptive multiscale analyses were 30% more efficient than full-domain multiscale analyses. The GMC sacrifices some accuracy in calculated local fields by assuming a low-order displacement field. More accurate microscale behavior can be obtained by using the highidelity GMC (HFGMC) at a significant computational cost. Proper orthogonal decomposition (POD) order-reduction methods were applied to the ensuing HFGMC sets of simultaneous equations as a means of improving the efficiency of their solution. A Galerkin-based POD method was used to both accurately and efficiently represent the HFGMC micromechanics relations for a linearly elastic E-glass/epoxy composite for both standalone and multiscale composite analyses. The computational efficiency significantly improved as the repeating unit cell discretization increased (10-85% reduction in computational runtime). A Petrov-Galerkin-based POD method was then applied to the nonlinear HFGMC micromechanics relations for a linearly elastic E-glass/elastic-perfectly plastic Nylon-12 composite. The use of accurate order-reduced models resulted in a 4.8-6.3x speedup in the equation assembly/solution runtimes (21-38% reduction in total runtimes). By appropriately discretizing model domains and enhancing the efficiency of lower length scale calculations, the goal of performing highidelity multiscale analyses of composites can be more readily realized.

The Effective Continuum Micromechanics Analysis Code (EC-MAC) was developed for predicting effective properties of composites containing multiple distinct nanoheterogeneities (fibers, spheres, platelets, voids, etc.) each with an arbitrary number of coating layers based upon either the modified Mori-Tanaka method (MTM) and self consistent method (SCM). This code was used to investigate the effect of carbon nanofiber morphology (i.e., hollow versus solid cross-section), nanofiber waviness, and both nanofiber-resin interphase properties and dimensions on bulk nanocomposite elastic moduli. For a given nanofiber axial force-displacement relationship, the elastic modulus for hollow nanofibers can significantly exceed that for solid nanofibers resulting in notable differences in bulk nanocomposite properties. The development of a nanofiber-resin interphase had a notable effect on the bulk elastic moduli. Consistent with results from the literature, small degrees of nanofiber waviness resulted in a significant decrease in effective composite properties. Key aspects of nanofiber morphology were characterized using transmission electron microscopy (TEM) images for VGCNF/vinyl ester (VE) nanocomposites. Three-parameter Weibull probability density functions were generated to describe the statistical variation in nanofiber outer diameters, wall thicknesses, relative wall thicknesses, visible aspect ratios, and visible waviness ratios. Such information could be used to establish more realistic nanofiber moduli and strengths obtained from nanofiber tensile tests, as well as to develop physically motivated computational models for predicting nanocomposite behavior. This study represents one of the first attempts to characterize the distribution of VGCNF features in real thermoset nanocomposites. In addition, the influence of realistic nanoreinforcement geometries, distinct elastic properties, and orientations on the effective elastic moduli was addressed. The effect of multiple distinct heterogeneities, including voids, on the effective elastic moduli was investigated. For the composites containing randomly oriented wavy vapor grown carbon nanofibers (VGCNFs) and voids, the predicted moduli captured the essential character of the experimental data, where the volume fraction of voids was approximated as a nonlinear function of the volume fraction of reinforcements. This study should facilitate the development of multiscale materials design by providing insight into the relationships between nanomaterial morphology and properties across multiple spatial scales that lead to improved macroscale performance.

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