Title page for ETD etd-06112005-183452

Type of Document Dissertation
Author Breitzman, Timothy Donald
Author's Email Address tbreitz@math.lsu.edu
URN etd-06112005-183452
Title Multiscale Strain Analysis
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Robert Lipton Committee Chair
Ambar Sengupta Committee Member
Lawrence Smolinsky Committee Member
Padmanabhan Sundar Committee Member
Robert Perlis Committee Member
Stephen Shipman Committee Member
Grover Waldrop Dean's Representative
  • fiber reinforced composite
  • homogenization
  • corrector theory
  • prestress
  • multi scale analysis
Date of Defense 2005-05-04
Availability unrestricted
The mathematical homogenization and corrector theory relevant to prestressed heterogeneous materials in the linear-elastic regime is discussed. A suitable corrector theory is derived to reconstruct the local strain field inside the composite. Based on this theory, we develop an inexpensive numerical method for multi scale strain analysis within a prestressed heterogeneous material. The theory also provides a characterization of the macroscopic strength domain. The strength domain places constraints on the homogenized strain field which guarantee that the actual strain in the heterogeneous material lies inside the strength domain of each material participating in the structure.
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