## On The Nonlinear Mechanics of Carbon Nano-Structures Using The
Consistent
Atomic-scale Finite Element Method

Eric Mockensturm, Mechanical Engineering, Penn State

In the present work, a new multiscale modeling technique called the
Consistent Atomic-scale Finite Element (CAFE) method is introduced.
Unlike traditional approaches for linking the atomic structure to its
equivalent continuum, this method directly connects the atomic
degrees of
freedom to a reduced set of finite element degrees of freedom without
passing through an intermediate homogenized continuum. As a result,
there is
no need to introduce stress and strain measures at the atomic level. The
Tersoff-Brenner interatomic potential is used to calculate the
consistent
tangent stiffness matrix of the structure. In this finite element
formulation, all local and non-local interactions between carbon
atoms are
taken into account using overlapping finite elements. In addition, a
consistent hierarchical finite element modeling technique is
developed for
adaptively coarsening and refining the mesh over different parts of the
model. This process is consistent with the underlying atomic
structure and,
by refining the mesh, molecular dynamic results will be recovered. In
contrast with most other multiscale methods, there is no need to
introduce
artificial boundaries for coupling atomistic and continuum regions. The
applicability of the method is shown with several examples of
deformation of
carbon nanostructures subjected to different loads and boundary
conditions.