In this thesis a microdynamics theory of structured solids is formulated on the basis of probabilistic functional analysis. The theory which is developed on the principles of probabilistic micromechanics, introduces from the onset spatial and temporal scales relevant in the dynamic analysis. A general formulation of the microdynamics of a three-dimensional solid is given in terms of an abstract dynamical system; the analysis is then specialized to the kinematic subspace of the general state space, whereby the former is found to possess the topological structure of a Hilbertian-Sobolev space. / The abstract dynamical system in the microdynamics theory is developed explicitly for the wave propagation in a semi-infinite bar of a polycrystalline solid with an arbitrary cross-section. The microstructure of the solid is taken to consist of cubic grains with random physical properties. The existence of an internal and a macroscopic time is postulated, which permits the formulation of the evolution of the wave motion first in a one-dimensional solid by means of a four parametric Markovian operator having a semi-group property. This model of the cubic solid structure is shown to be asymptotically equivalent to a "generalized wave equation" of the continuum theory. A more general model of the wavefront evolution for a three-dimensional solid is then given in terms of a super-martingale (parametrized by the macrotime) on a generalized random field. / It is shown that numerical results for the wave propagation in a discrete solid in accordance with the new microdynamics theory can be obtained by the application of the Monte-Carlo simulation method. A comparison of these results with known classical and random continuum theories is given.

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Thesis (Ph.D.)--University of Iowa, 2009. / Includes separate files for thesis supplements. Thesis supervisor: David E. Stewart. Includes bibliographical references (leaves 107-109).