3D Simulation of Representative Volume Element for Use in Multiscale FEM

Abstract

To closely follow material behaviour in a FE model, a numerical model of the material at a small length-scale can be used instead of material constants. The model of the lower length-scale is run at each integration point in the macroscale model, thereby coupling the models of both length-scales into one large numerical model. This approach is called multi-scale modelling. A three dimensional FE model of the grain structure of a bi-crystalline metal is developed. The model is aimed towards use as mesostructure model used in multi-scale FE computations. Since multi-scale models are computationally very expensive, the entire model was programmed in Fortran to maximize efficiency. The model automatically generates a random 3D grain structure using the Voronoi algorithm. The grain structure is subsequently discretized using a structured, regular grid. Even though the grid geometry is completely decoupled from the grain structure geometry, the model precision is increased by allowing the material properties to vary between integration points within elements, i.e. allowing grain boundaries within an element. The generated model assumes the mesostructure to consist of two grain phases, each phase being linear elastic. Data files for use with the 3D visualization tool Paraview are generated. A parameter study is carried out to study the resulting mesostructure model