ICAMS / Interdisciplinary Centre for Advanced Materials Simulation

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Upscaling via atomic coarse-graining: the problem of a seamless scale transition in concurrent multiscale methods

Date: 11.07.2008
Place: 2nd GAMM Seminar on Multiscale Material Modelling, University of Stuttgart

Bernhard Eidel

Among concurrent multiscale approaches in nanomechanics the quasicontinuum (QC) method is a prominent version of a bottom-up method aiming at a seamless link of atomistic with larger length scales. The main building blocks of the QC method are (i) a coarse-graining from fully atomistic resolution via kinematic constraints along with (ii) numerical integration or lattice summation rules, where (iii) the spatially adaptive resolution is directed by a suitable refinement indicator. This contribution deals with a review of different versions of the QC method, [1]{[3], with a special focus on the intended seamless scale transition and the arrangements taken to reach that goal. The first version of the QC method [1] is faced with ghost forces, i.e. spurious forces arising at the boundary between local regions, subject to the Cauchy-Born-Rule (CBR), and nonlocal regions of fully atomistic resolution. A remedy against these artifacts at the coupling-interface is to introduce static correction forces, which are not derivable from a correction potential energy, i.e. they are not conservative. The fully-nonlocal QC version of Knap and Ortiz [2] avoids the CBR and thus eliminates discrete interfaces between regions of different physical description. A force-based procedure as advocated in [2] sacrifices the existence of an energy-functional. In order to endow the fully nonlocal QC method with a variational structure, in [3] an energy-based procedure is applied starting from a well-defined total potential. We analyze these QC versions with respect to inherent modelling and numerical errors. We discuss different arrangements to avoid or to control spurious forces occurring at discrete interfaces in [1] or in a distributed manner in [2] and [3]. Finally, we showcase the promising capacity of the present QC method [3] to effectively reduce the prohibitive computational expense of fully atomistic resolution while faithfully simulating the materials response in significant details.

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