Coarse-Graining and Renormalization of Atomistic Binding Relations and Universal Macroscopic Cohesive Behavior

Abstract

We present two approaches for coarse-graining interplanar potentials and determining the corresponding macroscopic cohesive laws based on energy relaxation and the renormalization group. We analyze the cohesive behavior of a large---but finite---number of interatomic planes and find that the macroscopic cohesive law adopts a universal asymptotic form. The universal form of the macroscopic cohesive law is an attractive fixed point of a suitably-defined renormalization-group transformation.

15 pages, 6 figures, submitted to the Journal of the Mechanics and Physics of Solids

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