Multiscale materials science: a mathematical approach to defects, effective global and local behaviors and uncertainty

Abstract

The presence of numerous length-scales in material science problems represents a daunting challenge for numerical simulation. Quantifying the effects of defects, and more generally any uncertainty arising from data, discretization, and the mechanical model for an associated numerical method has become an increasingly important aspect of multiscale analysis. Such studies open the way to assessing the effective global and local behaviors of materials, and to quantifying the fluctuations around the mean response. The goal of this proposal is to investigate deterministic and stochastic numerical analyses for uncertainty quantification for a class of problems in computational material science. Such an analysis depends crucially upon (and integrates) a mathematical analysis and a multiscale mechanical model, and forms the basis of next generation predictive materials modeling and simulation. The project plan is to investigate the influence of essentially unknown, or random, parameters within non-periodic homogenization, from the viewpoint of both the underlying mechanical model and the associated numerical analysis.

Document Details

Document Type
DoD Grant Award
Publication Date
Jul 28, 2017
Source ID
FA95501710294

Entities

People

  • Claude Le Bris

Organizations

  • Air Force Office of Scientific Research
  • United States Air Force
  • École des Ponts ParisTech

Tags

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Computational Modeling and Simulation
  • Educational Psychology