Recent years have witnessed an increasing interest in polymer-based hollow particle filled composites resulting in a large number of analytical and experimental research efforts. Such materials, known as syntactic foams, are lightweight and highly damage tolerant composites used as core materials in sandwich structures for marine, aeronautical, and space applications. Improving the reliability of syntactic foams for these applications requires a thorough understanding of microstructure-property relationships, particle-matrix interfacial behavior, and the effect of water uptake mechanisms on the mechanical responses of syntactic foams.

In this dissertation, a novel approach based on a differential scheme is employed to analyze the linear elastic and viscoelastic behavior of syntactic foams. This method allows to extrapolate the mechanical properties of an infinitely dilute dispersion of hollow particles in the matrix material to high inclusion volume fractions. For the viscoelastic problem, the elasticity-viscoelasticity correspondence principle is used to predict storage modulus and loss tangent in a wide frequency range of mechanical vibrations from the elastic solution. This method provides useful insights into the role of particle volume fraction and wall thickness in tailoring syntactic foam properties. The approach can be used to analyze the mechanical properties of syntactic foams for as-fabricated and water exposed testing conditions. Deionized and salt water environments are used to study the effect of moisture absorption on the elastic properties of syntactic foams. Theoretical predictions are validated with experimental results and numerical analysis on sixteen compositions of as-fabricated vinyl ester-glass syntactic foams and generally show close agreement. In addition, these analytical findings can be used to interpret experimental data on water exposed systems elucidating the role of water in determining the flexural response of such composites.

Moreover, two different techniques are used to extend intrinsic limitations to previous approaches by accounting for the effect of matrix-particle debonding and particle-to-particle elastic interactions on the mechanical response of syntactic foams. Matrix-particle debonding is modeled by spherical-cap cracks at the matrix-particle interface. A series solution based on the Galerkin method is used to solve the problem of a single hollow inclusion dispersed in an infinite matrix. Particle-to-particle elastic interactions are studied by using a multi-pole series expansion combined with the Boussinesq-Papkovich stress function approach. For every studied problem, numerical results are in good agreement with those obtained from finite and boundary element analyses.