Computational Method for Atomistic-Continuum Homogenization
Final rept. Nov 2001-Nov 2002
ARMY RESEARCH LAB ABERDEEN PROVING GROUND MD
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The homogenization method is used as a framework for developing a multiscale system of equations involving atoms at zero temperature at the small scale and continuum mechanics at the very large scale. The Tersoff-Brenner Type II potential Tersoff J. Empirical Interatomic Potential for Carbon, With Applications to Amorphous Carbon. Physical Review Letters. vol. 61, no. 25, pp. 2879-2882, 19 December 1988 Brenner, D. W. Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of Diamond Films. Physical Review B, vol. 42, no. 15, pp. 94589471, 15 November 1990 is employed to model the atomic interactions while hyper elasticity governs the continuum A quasi-static assumption is used together with the Cauchy-Born approximation of enforce the gross deformation of the continuum on the positions of the atoms. The two-scale homogenization method establishes coupled self-consistent variational equations in which the information at the atomistic scale, formulated in terms of the Lagrangian stiffness tensor, concurrently feeds the material information to the continuum equations. Analytical results for a one-dimensional molecular wire and numerical experiments for a two-dimensional graphene sheet demonstrate the method and its applicability.
- Atomic and Molecular Physics and Spectroscopy