Computational Contact Mechanics

Stresses in a contact area loaded simultaneously with a normal and a tangential force. Stresses were made visible using photoelasticity.

Welcome to this learning project about computational contact mechanics!

## Contents

* 1 Introduction
* 1.1 Project metadata
* 1.2 Content summary
* 1.3 Goals
* 2 Contents
* 2.1 Syllabus and Learning Materials
* 2.2 Assignments
* 3 Textbooks and References
* 3.1 Textbooks
* 4 Physical Principles and Applications
* 4.1 References

## Introduction

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Computational Contact Mechanics deals with problems related to contact problems in the area of classical mechanics using computational means (like finite or boundary element methods). With increase in computational power, significant progress has been made towards robust numerical solutions to complicated contact problems. Owing to the complex nonlinear nature of contact,theoretical solutions are restricted to simple scenarios like Hertzian contact etc.

### Project metadata

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| Educational level: this is a tertiary (university) resource.

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| Subject classification: this is an engineering resource.

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* Suggested Prerequisites:
* Linear algebra
* Partial differential equations
* Nonlinear finite elements
* Continuum mechanics
* Contact mechanics
* Time investment: 6 months
* Portal: Engineering and Technology
* School: Engineering
* Department: Mechanical engineering
* Level: Senior year undergraduate and graduate students

### Content summary

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This is an introductory course on basics of computational contact mechanics and addresses problems of contact between two or more solid bodies. Nonlinearities can be caused by changes in geometry or be due to nonlinear material behavior. Both types of nonlinearities are covered in this course.

### Goals

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This learning project aims to.

* provide the mathematical foundations for formulation of contact problems using the finite element method
* expose students to some of the recent trends and research areas in contact mechanics

## Contents

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Syllabus and Learning Materials

### Syllabus and Learning Materials

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1. Mathematical Preliminaries

Assignments, tests and quizzes

### Assignments

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## Textbooks and References

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### Textbooks

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* A Guide for Engineers to Computational Contact Mechanics by G. Zavarise, P. Wriggers and U. Nackenhorst, The TCN series on simulation based engineering and sciences, 2006, ISBN-13 978-88-95176-00-0.
* Computational Contact Mechanics by P. Wriggers, Springer, 2002, ISBN-13 978-3-540-32608-3
* Computational Contact and Impact Mechanics by T. A. Laursen, Springer, 2002, ISBN-13 978-3-662-04864-1
* Contact Mechanics and Friction. Physical Principles and applications by V.L. Popov, 2nd Edition, Springer, 2017, Chapter 19,

## Physical Principles and Applications

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### References

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* Nonlinear Finite Element Analysis:
* J. N. Reddy (2004), An Introduction to Nonlinear Finite Element Analysis, Oxford University Press
* T. Belytschko, W. K. Liu, and B. Moran (2000), Nonlinear Finite Elements for Continua and Structures, John Wiley and Sons
* T. J. R. Hughes (2000), The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publications
* Finite Element Analysis:
* K-J. Bathe (1996), Finite Element Procedures, Prentice-Hall
* J. N. Reddy (1993), An Introduction to the Finite Element Method, McGraw-Hill
* O. C. Zienkiewicz and R. L. Taylor (2000), The Finite Element Method: Volume 2 Solid Mechanics, Butterworth-Heinemann
* S. C. Brenner and L. R. Scott (2007), The mathematical theory of finite element methods, vol. 15 of Texts in Applied Mathematics, Springer-Verlag
* Boundary Element Method:
* R. Pohrt and Q. Li, Complete boundary element formulation for normal and tangential contact problems, Phys Mesomech (2014) 17: 334. https://doi.org/10.1134/S1029959914040109
* BEM for adhesive contacts: Popov, V.L., Pohrt, R. & Li, Q. Strength of adhesive contacts: Influence of contact geometry and material gradients, Friction (2017) 5: 308. https://doi.org/10.1007/s40544-017-0177-3
* BEM for Functionally Graded Materials: Li, Q. & Popov, V.L. Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materialsComput Mech (2017). https://doi.org/10.1007/s00466-017-1461-9
* Continuum Mechanics:
* A.J.M Spencer (2004), Continuum Mechanics, Dover Publications.
* L.E. Malvern (1969), Introduction to the Mechanics of a Continuous Medium, Prentice-Hall
* Mathematics:
* B. Daya Reddy (1998), Introductory Functional Analysis: With applications to boundary value problems and finite elements. , Springer-Verlag

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