Atomistic-Continuum Coupling based on a Variationally Consistent Quasi-Continuum (QC) Method with Energy-Sampling in Clusters
Nanoindentation into fcc single crystalline aluminium. Top: cross-sectional view of the initial QC mesh with fully atomistic resolution in the region of dislocation nucleation. Bottom: dislocation microstructure.
Associated people
B. Eidel, A. Stukowski (LLNL, USA), J. Schröder
Abstract
The quasi-continuum (QC) method is a prominent example of a bottom-up, concurrent multiscale method aiming at a seamless link of atomic with continuum length scales. This aim is achieved by three main building blocks (i) a coarse-graining of fully atomic resolution via finite element discretization in order to reduce the number of degrees of freedom. Fully atomic resolution is retained at hot spots of inelastic deformations like at crack tips, at defect cores or alike, whereas a finite element coarse-graining is applied in regions of purely elastic deformation. (ii) An approximation of the energy/forces in coarse-grained regions via numerical quadrature which avoids the explicit computation of the site energy of each and every atom. (iii) Adaptivity, i.e. spatially adaptive resolution, is necessary to provide full atomic resolutions in regions of evolving or moving inelastic deformations like in crack propagation or microstructural evolution.
In [Eidel & Stukowski 2009] we develop a novel QC approach aiming at a truly seamless transition from the atomic to the continuum description of crystalline solids at zero temperature. It heavily draws on the framework proposed by Knap and Ortiz (2001). Opposed to Knap and Ortiz, the energy instead of forces is subject to a cluster based sampling scheme with adaptive resolution. We show that only the present ansatz endows the QC theory with a variational structure. The fully nonlocal methodology is assessed in nanoindentation into an fcc single crystal. Compared to the fully atomistic counterpart of lattice statics, the coarse-grained atomistic description with adaptive resolution achieves good agreement with respect to the force-displacement curve, the load-level and locus of dislocation nucleation and the dislocation microstructure for a small fraction of the computational costs. The figure shows the dislocation microstructure below the surface of an fcc aluminum single crystal which is subject to ball indentation at the nanoscale.
More recent research has been concerned with free surface relaxations of nano-structures in collaboration with N.V. Prajapati (RUB). Ongoing research activities are focused on modeling extensions of the QC but also with the development of novel numerical features for the method.