Ein Mehr-Skalen-Ansatz zur Modellierung quasi-spröden Materialversagens
Final Report Abstract
The objective of the present project is to understand the material failure phenomena at a fundamental level. Therefore, we couple a fine-scale model with a coarse-scale model. The coarse-scale model is a finite-element model while the fine-scale model is either a FEM-model or an atomistic model. A homogenization approach is used in the absence of a macroscopic crack while a concurrent adaptive multiscale method for quasi-static crack growth has been developed. The idea is to contain the crack tip in the fine-scale region and model the rest of the region by the coarse-scale. The extended finite element method or the phantom node method is used to model the crack in the coarse scale region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster - for an atomistic fine-scale model - is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the model behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom-atom interactions. The method is implemented in two dimensions. The results are compared to the results obtained from pure atomistic simulations; they show excellent agreement. Keywords: multiscale, adaptivity, refining, coarsening, phantom node method, molecular statics, virtual atom cluster.
