The current formulation of the quasicontinuum (QC) method relies on a static triangulation of the reference crystal configuration. This computational mesh needs to encompass a wide range of spatial resolutions, from fully atomistic at defect cores, to continuum-like in defect-free regions. Moreover, it must continuously adapt to the structure of the deformation field, so as to return the least possible potential energy for a fixed number of nodes. In the implementations of the QC method to date, the mesh adaption procedure has been based on empirical indicators. We present a variational adaption Lagrangian-Eulerian (VALE) method for the QC method. In this approach, the computational mesh is factored directly into the description of the energetics of the crystal. Therefore, the energy minimizer determines not only the equilibrium configuration of the crystal, but also the optimal configuration of the computational mesh. We apply the VALE-QC method to the investigation of a wide array of problems, from nanoindentation to crack tips.
展开▼
