W. Z. Shan and U. Nackenhorst
Computational Mechanics, 46, 577–596 (2010).
This contribution introduces an adaptively coupled finite element (FE)-molecular dynamics (MD) model based on the Quasicontinuum (QC) method. The idea for obtaining constitutive laws from the underlying lattice structure (local QC model) will be discussed in detail. The outline of the formulation for the quasi-static MD model (nonlocal QC model) will also be derived in the same mathematical structure. A new type of element is proposed to solve the boundary problems and to couple the FE and MD models. The interpolation techniques for the atomic stress and strain fields are introduced. A two-step adaptive mechanism is applied to the multiscale model, including the mesh refinement step for the FE model and the FE-MD conversion step. A 3D nanoindentation example is used for demonstrating accuracy and the efficiency of the coupled FE-MD model at the end.