Identifier

etd-07092008-073929

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The dissertation provides new multiscale methods for the analysis of heterogeneous media. The first part of the dissertation treats heterogeneous media using the theory of linear elasticity. In this context, a methodology is presented for bounding the higher order moments of the local stress and strain fields inside random elastic media. Optimal lower bounds that are given in terms of the applied loading and the volume (area) fractions for random two-phase composites are presented. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to applied loads. The second part of the dissertation treats heterogeneous media using the peridynamic formulation of nonlocal continuum mechanics. In this context, a multiscale analysis method is presented for capturing the dynamics inside fiber-reinforced composites at both the structural scale and the microscopic scale. The method provides a multiscale numerical method with a cost that is much less than solving the full micro-scale model over the entire macroscopic domain.

Date

2008

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Lipton, Robert

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