SUMMARY

This thesis focuses on the micromechanical modeling of particulate viscoelastic composite materials in the quasi-static frequency domain to approximate macroscopic damping behavior and has two main objectives. The first objective is the development of a robust frequency dependent multiscale model. For this purpose, the self-consistent (SC) mean-field micromechanical model introduced by Cherkaoui et al [J. Eng. Mater. Technol. 116, 274-278 (1994)] is extended to include frequency dependence via the viscoelastic correspondence principal. The quasi-static model is then generalized using dilute strain concentration tensor formulation and validated by comparison with complex bounds from literature, acoustic and static experimental data, and established models. The second objective is SC model implementation as a tool for the design of high loss materials. This objective is met by integrating the SC model into a Compromise Decision Support Protocol (CDSP) to explore the microstructural design space of an automobile windshield. The integrated SC-CDSP design space exploration results definitively indicate that one microstructural variable dominates structure level acoustic isolation and rigidity: negative stiffness inclusions. The work concludes with a detailed description of the fundamental mechanisms leading to negative stiffness behavior and proposes two negative stiffness inclusion designs.