Multiscale materials science: A mathematical approach to defects, effective global and local behaviors and uncertainty
Abstract
Project summary 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. 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. It is the aim of this interdisciplinary project to develop new mathematical and numerical tools, including probabilistic approaches, to address the current challenging problems of interest in materials science. In particular, one major feature of the proposed project will be to address questions using both deterministic approaches and probabilistic approaches. It is our belief that a satisfactory theoretical understanding of ideal perfect materials has now been achieved along with the design of reasonably efficient numerical approaches for the simulation of those. It is however a pending challenge to understand, model, simulate and control real materials in all their inevitable imperfections. Issues such as the modeling of defects, of how fatigue and aging affect the characteristic of materials, are not so well understood. Clearly, research in this matter requires skills diverse in nature. The present proposed project aims at suggesting mathematical approaches that can help in this endeavor. This project is a continuation of previous projects carried out in the same context. Al- though related to the topics explored in the previous proposals, the topics that will be explored in this upcoming period are new. In each of the research directions we propose, we have already obtained some preliminary results, which we consider sufficiently promising to now expect significant progress for numerical simulation techniques.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512777
Entities
People
- Claude Le Bris
Organizations
- Office of Naval Research
- United States Navy
- École des Ponts ParisTech