Ceramic Matrix Composites (CMC) are attractive material systems for structural applications where resistance to intermediate (700 0C-950 0C) and high temperatures (900 0C-1400 0C) is required and low density is desired. There are currently barriers to a more widespread adoption of CMCs which include less robust simulation tools, which this dissertation seeks to address. A novel unified reduced order homogenization model for initial quasi-static, creep, and fatigue loading of SiC/SiC CMCs at intermediate and high temperatures is proposed. Driven by a single set of parameters, the model can seamlessly transition between initial quasi-static, creep, and fatigue regimes while capturing the complex material response of SiC/SiC CMCs. The reduced order homogenization approach provides a robust and efficient computational platform for analyzing composite behavior. Continuum damage mechanics provides the basis for the initial brittle CMC behavior while a hybrid damage-viscoplasticity model combined with an oxidation driven crack sealing effect drives the time-dependent brittle-ductile material behavior at high temperatures. A temporal multiscale approach extends the spatial multiscale model into fatigue regime at high temperatures, avoiding the computational complexity of modeling each cycle individually. At intermediate temperatures, a one-dimensional model based on the slow crack growth model originally proposed by Iyengar and Curtin is generalized to three dimensions focusing on a woven composite architecture. For this oxidation-assisted rupture model, the constitutive equation in the axial tow direction is governed by the continuum damage mechanics variant of the slow crack-growth model and the availability of oxygen to fibers, which in turn depends on the initial matrix pores and subsequent matrix cracking. The model is verified on two SiC/SiC material systems, S200H and GEA SMI, in both initial quasi-static and time-dependent loading regimes at both high and intermediate temperatures.

We develop a dual-purpose damage model (DPDM) that can simultaneously model intralayer damage (ply failure) and interlayer damage (delamination) as an alternative to conventional practices that models ply failure by continuum damage mechanics (CDM) and delamination by cohesive elements. From purely computational point of view, if successful, the proposed approach will significantly reduce computational cost by eliminating the need for having double nodes at ply interfaces. At the core, DPDM is based on the regularized continuum damage mechanics approach with vectorial representation of damage and ellipsoidal damage surface. Shear correction factors are introduced to match the mixed mode fracture toughness of an analytical cohesive zone model. A predictor-corrector local-nonlocal regularization scheme, which treats intralayer portion of damage as nonlocal and interlayer damage as local, is developed and verified. Two variants of the DPDM are studied: a single- and two- scale DPDM. For the two-scale DPDM, reduced-order-homogenization (ROH) framework is employed with matrix phase modeled by the DPDM while the inclusion phase modeled by the CDM. The proposed DPDM is verified on several multi-layer laminates with various ply orientations including double-cantilever beam (DCB), end-notch-flexure (ENF), mixed-mode-bending (MMB), and three-point-bending (TPB). The simulation is executed in the platform of FOOF (Finite element solver based on Object-Oriented Fortran). The objective of FOOF is to develop a new architecture of the nonlinear multiphysics finite element code in object oriented Fortran environment. The salient features of FOOF are reusability, extensibility, and performance. Computational efficiency stems from the intrinsic optimization of numerical computing intrinsic to Fortran, while reusability and extensibility is inherited from the support of object-oriented programming style in Fortran 2003 and its later versions. The shortcomings of the object oriented style in Fortran 2003 (in comparison to C++) are alleviated by introducing the class hierarchy and by utilizing a multilevel programming style.