Mixed finite element and atomistic formulation for complex crystals
E. B. Tadmor, G. S. Smith, N. Bernstein and E. Kaxiras
Physical Review B, 59, 235–245 (1999).


A general formulation for the analysis of complex Bravais crystals using
atomic energy functionals embedded within a finite element framework is
presented. The method uses atomistic potentials to determine the constitutive
response of the system. Unlike traditional finite element methods, the
nonlinear elastic effects, the symmetries of the underlying crystal, and the
possibility of uniform structural phase transformations are naturally included
in this formulation. Explicit expressions for empirical energy functionals
with separable two- and three-body potentials, and semiempirical tight-binding
energy functionals with two-center integrals are presented. A simple
application to silicon underscores the importance of including internal
relaxation in a finite element treatment of a complex crystal. In a
forthcoming companion paper, the method presented here is applied to the
nanoindentation of silicon.