Multiscale Modeling of Materials: Joining Atomistic Models with Continuum Mechanics

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 23)


The goal in multiscale modeling is to predict the performance and behavior of heterogeneous materials in which there are several relevant and widely disparate length scales. Due to the great complexities that are involved, the task of developing a multiscale model is usually referred to as a grand challenge problem. The complexities that are involved are clear: At the atomic scale electrons govern the interactions among atoms in a material, and thus quantum-mechanical effects are important and must be taken into account. At the same time, at the macroscopic or engineering scale, forces that arise from macroscopic stresses and/or temperature gradients are the factors that control the performance of materials. At the intermediate length scales, defects such as dislocations control the mechanical properties of materials up to tens of micrometers, while large collections of such defects, including grain boundaries, govern their mesoscopic properties up to length scales that are of the order of hundreds of micrometers. Coupling of all of these length scales would not have been possible, had it not been for the tremendous advances in the advent of ever more powerful, massively-parallel computers, and the great advances that have been made in the theoretical understanding of materials and their properties. The emerging multiscale methodology demonstrates how coupling of atomistic and continuum approaches results in more predictive power than either approach offers alone.

An interesting and very useful aspect of multiscale modeling is the fact that, it is a multidisciplinary field that brings together scientists from many disciplines. The development of a multiscale model of any phenomenon that deals with one or more aspect of materials’ properties should, in principle at least, involve chemists and chemical engineers, applied physicists and mathematicians, and continuum mechanicians.


Molecular Dynamic Slip Plane Atomistic Simulation Multiscale Approach Atomistic Computation 
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© Springer-Verlag New York, Inc. 2003

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