Tobias Willerding

Abstract

This thesis is about multiscale simulation of phase transformation in metals. Multiscale simulation is the simultaneous use of two or more models in order to have phenomena of different length or time scale in one simulation. Phase transformation between different lattice structures plays an important role in the formation of metals, e.g. iron or titanium. It is, therefore, of interest to simulate phase transformation in a multiscale context. In this thesis, a multiscale method for the simulation of phase transformation in metals is developed. Continuum mechanics, represented by the finite element method, is coupled with atomistics, represented by molecular dynamics. The goal is to simulate phase transformation in metals between different lattice structures such as body-centered cubic, face-centered cubic and hexagonal close-packed structure. As phase transformation requires an internal restructuring of the molecular structure, traditional multiscale methods cannot be used as these require fixed coupling at the interface between coarse scale and fine scale and very often also in the coarse scale by using the Cauchy(-Born) rule. In order to overcome these problems, a combined hierarchic-partitioned-domain method is proposed that consists of two parts. On the finite element level, a hierarchic method based on the FE2-method is used with molecular dynamics simulations as subproblems, one subproblem at each Gauss integration point. The partitioned-domain part of the method consists of dividing the domain into two parts: a molecular dynamics part and a finite element part. A part of the atoms are put into a box with the shape of a parallelepiped and with periodic boundary conditions. This box is linked to the movement of the finite element nodes.