Development of a Nonperiodic Homogenization Method for One-Dimensional Continua

Abstract

This work describes a one-dimensional? homogenization method that relaxes the usual assumption of periodicity of microscale displacements. As such this method is appropriate for studying materials with periodic as well as nonperiodic microstructure. Expected applications for the new method include composite rods with manufacturing variability (where material periodicity is destroyed) and rods composed of functionally graded materials. The method is validated through direct comparison with a known exact solution that being a rod with linearly varying axial rigidity. The method for this case is shown to be exact. Further application of the developed method to two different periodic materials is used to validate the usual periodic assumption employed in traditional homogenization methods.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2004
Accession Number
ADA424375

Entities

People

  • Michael J. Leany
  • Peter W. Chung
  • Raju Namburu

Organizations

  • United States Military Academy

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundaries
  • Boundary Value Problems
  • Composite Materials
  • Continuum Mechanics
  • Differential Equations
  • Displacement
  • Equations
  • Finite Element Analysis
  • Laminates
  • Materials
  • Mechanics
  • Microbalances
  • Military Research
  • Partial Differential Equations
  • Periodic Variations
  • Rigidity

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Nanocomposite Materials Science
  • Theoretical Analysis.