Part I (Efficient Endochronic Finite Element Analysis: an Example of a Cyclically Loaded Boron/Aluminum Composite): A convenient and efficient algorithmic tangent matrix approach has been developed for 3-D finite element (FE) analysis using the endochronic theory without a yield surface. The underlying algorithm for integrating the endochronic constitutive equation was derived by piecewise linearization of the plastic strain path. The approach was employed to solve a micromechanics boundary value problem of a cyclically loaded unidirectional boron/6061 aluminum composite. All the FE results consistently demonstrate superior numerical stability and efficiency of the proposed method. Extensions of the method to endochronic plasticity with a yield surface and to the plane stress case are also presented. Part II (Simple and Unified Finite Element Formulation for Doubly Periodic Models: Applications to Boron/Aluminum Composites): A simple and unified weak formulation and its convenient FE implementation have been proposed. The weak formulation is valid for any doubly periodic model under uniform 3-D macro-stress, and serves as a common rational foundation of different FE approaches. The algorithmic tangent matrix approach for the endochronic theory has been incorporated into the FE formulation to model isothermal, rate-independent plastic macro-deformation of unidirectional fibrous composites with idealized two-phase micro-structure and backed-out inelastic matrix properties. Methods for determining inelastic material parameters of the matrix have been established. Numerical results for a B/6061 AI composite subjected to on-axis and off-axis monotonic tensile loadings are in good agreement with experimental data. The micromechanics model also shows the potential for quantitative characterization of complicated cyclic behavior. Finally, some effects of model geometry on overall plastic response of the B/6061 AI composite are discussed from the viewpoint of theoretical-experimental correlation. / Ph. D.

A stress model of the filament-winding fabrication process, previously implemented in a finite element program, was improved. Pre- and post-processing codes were developed to make the program easier and more efficient to use. A program which is used to design filament wound composite rocket motor cases was modified to write a model file for the fabrication stress code in the pre-processing stage. The same code was altered to provide post-processing output in the form of graphic displays. Also, a new code was written to provide additional post-processing capability for the fabrication stress model. Verification of the model of the filament-winding process was performed by comparing experimental pressure and strain data, for the fabrication of a filament wound bottle, with results of an analytical model. The final analytical results using consecutive models of the filament wound bottle show reasonable agreement with experimental pressure and hoop strain data. The maximum difference in the analytical and experimental values in the pressure data was about 25% for the final winding stage. The difference was smaller during the winding progression. These results also show that the accuracy of the model depends heavily on the assumptions made for input parameters during modelling. The stiffness of the segmented steel mandrel, simulated by an effective modulus (degraded by segmentation), and the instantaneous laydown tension loss parameters significantly affected the results of the model. Including the effective modulus for the segmented mandrel in the model reduced the difference in the experimental and analytical pressure results by about 150%. The inclusion of instantaneous laydown tension loss in the model reduced the analytical-experimental difference by roughly 225%. These two parameters reduced the largest difference in the predicted pressure values from about 400% for the first model to around 25% for the final model. The fabrication stress model was coupled with the thermo-kinetic cure model to provide more accurate fiber motion tension loss analysis capability. The stress model was modified to use the thermo-kinetic model as a subroutine to calculate fiber motion tension loss using a two-dimensional analysis. The results of the qualitative verification show that fiber motion tension loss is more important in the later stages of winding than in the beginning stages which indicates that it may provide the needed accuracy in the final winding stages. / Master of Science