ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Multiscale modelling and simulation of surfaces in metallic nanostructures

Date: 16.05.2010
Place: ECCM 2010 - European Conference on Computational Mechanics, Paris, France

Bernhard Eidel
Nirav Prajapati

Free surfaces largely determine the mechanical properties and overall materials behaviour of crystalline nanostructures, which typically exhibit a large surface-to-volume ratio. Atoms residing at free surfaces feature an under-coordination and hence differ from their bulk counterparts. As a consequence, typical effects are observed at free surfaces like relaxation and reconstruction which influence problem sets in contact mechanics along with e.g. friction and wear. The key challenge in multiscale modelling of crystalline surfaces at the nanoscale is to consolidate the opposite requirements of accuracy and efficiency. More specifically, three main modelling requirements can be formulated; (i) a nonlocal theory must be employed in order to account for the under-coordination of atoms at or close to free surfaces; (ii) a coarse-grained description using e.g. finite elements is desirable for the sake of efficiency; (iii) a coarse-graining along with numerical quadrature must ensure that the collocation points for explicit energy-/force-calculation are directly located at surfaces as the region of interest. In view of these requirements, standard models and methods in discrete mechanics as well as in continuum mechanics exhibit major drawbacks. Fully atomistic resolution in molecular dynamics or molecular statics can achieve high accuracy by virtue of the nonlocal interatomic potentials employed, the computational burden however may become prohibitive. Continuum models in contrast, which accurately represent bulk material behaviour, fail to account for surface effects without the introduction of an internal length scale dependence. The present contribution aims to achieve predictive simulations of free surfaces of metallic solids. The proposed modelling approach is a 3d, fully nonlocal quasicontinuum method [1, 2, 3] which belongs to the class of concurrent multiscale methods [4, 5]. The method’s key feature of coarse-grained atomistics with adaptive resolution meets the above requirements (i)–(iii). Representative numerical tests assess the present method and showcase its capacity to account for free surface effects like relaxation and to simulate nano-contact problems in materials science and engineering with high accuracy and considerable efficiency.


[1] J. Knap, M. Ortiz: An analysis of the quasicontinuum method, J. Mech. Phys. Solids, 49 (2001) 1899–1923.
[2] B. Eidel, A. Stukowski: A variational formulation of the quasicontinuum method based on energy sampling in clusters, J. Mech. Phys. Solids, 57 (2009) 87–108.
[3] B. Eidel: Coupling atomistic accuracy with continuum effectivity for predictive simulations in materials research – the Quasicontinuum Method, Int. J. Mat. Res. (formerly Z. Metallkd.) 100 (2009) 11, 1503–1512.
[4] W. Curtin, R. E. Miller: Atomistic/continuum coupling in computational materials science, Modeling Simul. Mater. Sci. Eng. 11 (2003) R33–R68.
[5] R. E. Miller, E. B. Tadmor: A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods, Modeling Simul. Mater. Sci. Eng. 17 (2009) 053001.

Supporting information:

« back