| The dissertation develops a computational basis for modeling viscoelastic composite and porous materials. A two-dimensional model for a suitably oriented plane section through a composite (or porous) polymeric material is adopted in this research.; In the first stage of the research, a direct boundary integral method in the time domain is presented to solve the problem of an infinite, isotropic Kelvin (or Boltzmann) viscoelastic plane containing multiple randomly distributed, non-overlapping circular holes and perfectly bonded elastic inclusions. The holes and inclusions are of arbitrary size and the elastic properties of the inclusions can, in general, be different. The method is based on a direct boundary integral approach for the problem of an infinite elastic plane containing multiple circular holes and elastic inclusions, and a time stepping strategy.; However, this method suffers from the disadvantage that only constant viscoelastic Poisson's ratios can be considered, which is not realistic in practice. To deal with a more general situation, a complex variable boundary integral method based on the correspondence principle is developed. Up to date this method has been applied to solve the problem of an infinite (or finite) viscoelastic plane containing multiple circular holes. It is capable of accurately computing the stresses and displacements at any point and any time, without the need to consider a series of discrete time steps. It also enables the consideration of a variety of viscoelastic models. For the sake of illustration, examples are given for the cases that the viscoelastic solid responds as (i) a Boltzmann model in shear and elastically in dilatation, (ii) a Boltzmann model in both shear and dilatation, and (iii) a Burgers model in shear and elastically in dilatation. The accuracy and efficiency of the approach are demonstrated by comparing selected results with the solutions by the finite element method and by the time stepping boundary integral approach.; As an immediate application, the method is employed to determine the effective properties of viscoelastic porous materials. The effective deviatoric and volumetric creep compliance of the viscoelastic porous material is obtained by computing the mechanical response for a representative volume of the porous material. |
