Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior
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.
© 2002 Elsevier. Received 6 June 2001, Accepted 31 October 2001, Available online 11 December 2001. This work has been supported by Brown University's MURI Center for the "Design and Testing of Materials by Computation: A Multi-Scale Approach". We are grateful to Emily A. Carter, Emily A.A. Jarvis and R.L. Hayes for many useful discussions and suggestions, and for making available to us their research results prior to publication.