Cyclically loaded structures exhibit, over time, a degradation of material properties, commonly termed fatigue. Fatigue of materials has been estimated to cause 60-80% of the failures of mechanical components. Finite element method can be a cost-effective tool for investigating failure mechanisms, especially in the context of new and complex materials. Even though significant progress has been made, numerical modeling of structures under cyclic loadings remains difficult. The difficulties are associated with (i) the necessity of simulating a large number of cycles for capturing the long term change in the material and structural response and (ii) the necessity of taking into account the evolution of defects (e.g., cracks, voids). In this dissertation, we aim to address both issues.

To reduce the computational time for cyclically loaded structures, a so-called cycle jump technique is developed. The approach approximates the long term evolution of the response of a structure and eliminates the necessity of simulating all cycles in the loading path. It is found that a 60-70% reduction of computational time can be obtained with a small accuracy loss (on average less than 1%).

An object-oriented modeling frame is developed for simulating cyclic crack growth. The key feature is that various crack propagation criteria can be defined and coded based on any quantity available in the model. The capabilities of the modeling frame are demonstrated on a number of problems, including fracture mechanics specimens, multi-layered structures and systems with micro-structural features.

In particular, we investigate a new crack propagation criterion based on the accumulated plastically dissipated energy, integrated over a domain in front of the crack-tip. It is found that this simple criterion can capture both crack acceleration and retardation. Effects of the load ratio and tensile overloads, as captured by the implemented criterion, are found in qualitative agreement with experimental observations.

Next, the modeling frame is employed to replicate the formation of a crack observed in a thermal barrier coating (TBC) system. A parametric study is conducted to assess which material properties lead to the crack opening observed experimentally. A simple analytical procedure is proposed to improve the numerical modeling of the growth of the aluminum oxide layer in the TBC system.

Finally, a Monte-Carlo type computational procedure is implemented for predicting the effective elastic properties in materials assumed macroscopically isotropic. This computational approach is demonstrated on systems containing spherical particles. Both uncoated and coated particles are considered. The developed modeling frame is used to include random distributions of interfacial flaws between material phases.