Title page for ETD etd-07092008-073929

Type of Document Dissertation
Author Alali, Bacim
Author's Email Address alali@math.lsu.edu
URN etd-07092008-073929
Title Multiscale Analysis of Heterogeneous Media for Local and Nonlocal Continuum Theories
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Lipton, Robert Committee Chair
Adkins, William Committee Member
Neubrander, Frank Committee Member
Perlis, Robert Committee Member
Shipman, Stephen Committee Member
Goettert, Jost Dean's Representative
  • Multiscale Analysis
  • Heterogeneous Media
  • Peridynamics
  • Non-local Continuum Mechanics
  • Fiber-Reinforced Materials
  • Composite Materials
  • Failure Criteria
  • Load Transfer
  • Stress Concentrations
  • Optimal Strain Bounds
  • Optimal Stress Bounds
  • Field Fluctuations
  • Homogenization
Date of Defense 2008-06-25
Availability unrestricted
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.

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