Mathematical Problems in Micromechanics and Composite Materials

Abstract

This is the final technical report on ARO Contract DAAL03-89-K-0039, which began February 1, 1989 and terminated January 31, 1992. The scientific focus of this work is at the frontier where mathematics meets the materials sciences. Physically, we are concerned with the effective moduli of composites, the formation of fine scale structure in coherent phase transitions, and with oscillatory solutions of nonlinear partial differential equations from continuum. mechanics. Mathematically, we bring to bear a variety of tools including homogenization, the calculus of variations, and the theory of stochastic Processes. Our accomplishments include: (1) new bounds on the effective moduli of two-component and polycrystalline composites; (2) a new understanding of the role of surface energy in coherent phase transitions; and (3) rigorous results on the effective diffusivity due to a turbulent velocity field. The training of young scientists, both postdocs and students, has been a major part of our activity. composite materials; effective moduli; phase transitions; turbulent transport.

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Document Details

Document Type
Technical Report
Publication Date
Mar 26, 1992
Accession Number
ADA249584

Entities

People

  • Graeme W. Milton
  • Marco Avellaneda
  • Robert V. Kohn

Organizations

  • New York University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Composite Materials
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Elastic Materials
  • Elastic Properties
  • Fluid Dynamics
  • Fluid Flow
  • Geometry
  • Materials
  • Materials Science
  • Mathematical Models
  • Mechanics
  • Partial Differential Equations
  • Phase Transformations
  • Two Dimensional

Fields of Study

  • Physics

Readers

  • Materials Science and Engineering.
  • Research Science/Academic Research
  • Structural Health Monitoring of Composite Structures.