Multiscale Materials Science: A Mathematical Approach to Defects, Effective Global and Local Behaviors and Uncertainty

Abstract

The principal investigators for this grant performed computational and theoretical work focused on the construction of coarse approximations for problems with highly oscillatory coefficients. While satisfactory theoretical understanding of ideal perfect materials has been achieved along with the design of reasonably efficient numerical approaches to simulate them this research addresses the need to model, simulate and control real materials in all their inevitable imperfections. The attached report describes the success of the principal investigators to make theoretical and practical improvements to a numerical modeling, primarily to the approach posed by R. Cottereau in Numerical strategy for unbiased homogenization of random materials. This grant has resulted in the publication of 8 peer reviewed articles which are attached at the end of the attached report for ease of access.

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Document Details

Document Type
Technical Report
Publication Date
Sep 25, 2020
Accession Number
AD1110229

Entities

People

  • Claude Le Bris
  • F. Legoll
  • O. Gorynina

Organizations

  • École des Ponts ParisTech

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Value Problems
  • Calculus Of Variations
  • Composite Materials
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Simulations
  • Differential Equations
  • Finite Element Analysis
  • Materials
  • Materials Science
  • Mathematical Analysis
  • Mechanics
  • Numerical Analysis
  • Parallel Computing
  • Partial Differential Equations
  • Two Dimensional

Readers

  • Computational Fluid Dynamics (CFD)
  • Educational Psychology
  • Technical Research and Report Writing.