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. The goal of this proposal is to investigate for uncertainty quantification 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. The present proposal is focused on the modeling of defects.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. 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 thecharacteristic of materials, are not so well understood. Clearly, research in this matter requires skills diverse in nature. The present proposed project, the title of which could read as Beyond the diffusion equation: theory and numerics, aims at suggesting mathematical approaches that can help in this endeavor in the case of equations more complicated than purely diffusive equations.This project is a continuation of previous projects carried out in the same context, and funded by the ONR. Although related to the topics explored in the previous proposals, the topics that will be explored in this upcoming period are new.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 31, 2020
- Source ID
- N000142012691
Entities
People
- Claude Le Bris
Organizations
- Office of Naval Research
- United States Navy
- École des Ponts ParisTech