Partition of Unity Methods

12 An Introduction to Multiscale analysis with XFEM

Robert Gracie

Department of Civil and Environmental Engineering, University of Waterloo, Canada

12.1 Introduction

Many physical processes important to engineers and scientists are the result of phenomena occurring over multiscale length scales. For example, plasticity is governed by numerous phenomena simultaneously occurring across multiple scales. At the nanoscale (<10⁻⁹ m), plasticity is the motion of a crystal defect, called a dislocation, moving by the making and breaking of atomic bonds. At the sub-microscale (between m and m), dislocation-dislocation interactions dominate the plastic response of a single crystal. At the microscale (between m and m), grain shape and size play a defining role in the plastic response of a poly-crystalline material. At the scale of a component or a structure (> m), plastic response depends upon both the loads on the structure and the geometry of the structure. In order to fully understand the ...