Embedded active and passive devices has been increasingly used by in order to integrate more functions inside the same or smaller size device and to meet the need for better electrical performance of the component assemblies. Solder joints have been used in the electronic industry as both structural and electrical interconnections between electronic packages and printed circuit boards (PCB). When solder joints are under thermal cyclic loading, mismatch in coefficients of thermal expansion (CTE) between the printed circuit boards and the solder balls creates thermal strains and stresses on the joints, which may finally result in cracking. Consequently, the mechanical interconnection is lost, leading to electrical failures which in turn causes malfunction of the circuit or whole system. When a die is embedded into a substrate, Young's modulus of the die is larger than one of the core of the substrate and the CTEs of the die is smaller than those of the substrate. As a result, mismatch in coefficients of thermal expansions (CTE) between the substrate with the embedded device and the solder balls may increase. In the present study, finite element method (FEM) is employed to find out the stress and strain distribution of ball grid array(BGA) solders under thermal cycling. The ANAND model for viscoplasticity is employed for this purpose.

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.