Skip to Main Content
Partition of Unity Methods
book

Partition of Unity Methods

by Stéphane P. A. Bordas, Alexander Menk, Sundararajan Natarajan
October 2023
Intermediate to advanced content levelIntermediate to advanced
368 pages
12h 57m
English
Wiley
Content preview from 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 10 Superscript negative 8 m and 10 Superscript negative 6 m), dislocation-dislocation interactions dominate the plastic response of a single crystal. At the microscale (between 10 Superscript negative 6 m and 10 Superscript negative 4 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 (>10 Superscript negative 3 m), plastic response depends upon both the loads on the structure and the geometry of the structure. In order to fully understand the ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Wanted

Wanted

David Freemantle
Vue.js: Tools & Skills

Vue.js: Tools & Skills

James Hibbard, Maria Antonietta Perna, Ivaylo Gerchev, Michiel Mulders, David Bush

Publisher Resources

ISBN: 9780470667088Purchase Link