Abstract
AbstractThe efficient and accurate coupling of two dissimilar domains presents a major challenge, especially when wave propagation is considered. Overlap coupling methods are promising in the sense that spurious wave reflections can be avoided and loss of energy due to the coupling scheme can be minimized. However, the conservation properties and the proper physical representation of the forces depend on the precise formulation of the algorithm for coupling such dissimilar models. This is unlike that of coupling similar domains. We will demonstrate this with the help of numerical studies in continuum‐to‐continuum coupling and continuum‐to‐discrete coupling. Copyright © 2009 John Wiley & Sons, Ltd.
Highlights
The macroscopic behaviour of engineering materials is to a large extent determined by physical processes which occur at a scale that is one to several orders of magnitude smaller than the macroscopic scale of observation
More recently, constitutive relations have been derived at the macroscopic level which depart from micromechanical considerations at a lower scale, followed by subsequent upscaling
The domain is thought to consist of two subdomains, M and m, which are modelled using a continuum approach and a molecular dynamics approach, respectively
Summary
The macroscopic behaviour of engineering materials is to a large extent determined by physical processes which occur at a scale that is one to several orders of magnitude smaller than the macroscopic scale of observation. In the case of continuum-to-discrete transition, or vice versa, we have very different quantities: Classical notions like strains and stresses in the continuum model, but in the atomistic domain only quantities like displacements and the bonding energy make sense from a physics point of view These differences make that the precise form of the algorithm becomes more critical if we wish to properly preserve energy and avoid the appearance of non-physical forces when a wave propagates through the coupling zone. This is of particular importance since the characteristic space and time scales in the atomistic domain are much smaller than those in the continuum domain. Differences are highlighted which depend on the precise formulation, and the favourable properties of one formulation in terms of energy conservation for multiscale analyses are indicated
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