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