Analysis of Multi-Scale Phenomena in Heterogeneous Materials

Abstract

A new variational methodology is developed for computing optimal bounds on the stress inside thermoelastic composites. The method also provides tight bounds on the strength domains for random two phase elastic plastic composites. A second effort develops a global local infinite element method for problems with multiple length scales such as functionally graded thermal barrier coatings. The method consists of a global Galerkin scheme based upon the use of a small number of optimal local basis functions. The local bases are supported on sub domains of fixed diameter within the computational domain. A new class of optimal local bases are discovered that provide local approximations to the actual solution with exponentially decreasing error. For this choice the global Galerkin approximation converges exponentially with the coarse scale degrees of freedom.

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Document Details

Document Type
Technical Report
Publication Date
Feb 22, 2011
Accession Number
ADA548688

Entities

People

  • Robert Lipton

Organizations

  • Louisiana State University

Tags

Communities of Interest

  • Advanced Electronics
  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mathematics
  • Band Structures
  • Boundary Value Problems
  • Composite Materials
  • Composite Structures
  • Computational Science
  • Dielectric Permittivity
  • Differential Equations
  • Finite Element Analysis
  • Geometry
  • Materials
  • Materials Science
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Numerical Analysis
  • Two Dimensional

Readers

  • Operations Research
  • Structural Dynamics.