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 Contact mechanics!

Introduction

Contact Mechanics deals with problems arising due to two bodies (or media, in general) are in contact. The contact can be between two solids or two fluids or between a solid and fluid. Due to the nonlinear nature of contact, analytical solutions are derivable only for simple situations. However computational methods are being widely used today to deal with contact problems.

Project metadata

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

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

Content summary

This is an introductory course on 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

This learning project aims to.

• provide the mathematical foundations for analytical solutions to contact problems
• expose students to some of the recent trends and research areas in contact mechanics
• provides a foundation to further pursue a course on computational contact mechanics

Contents

Syllabus and Learning Materials Syllabus and Learning Materials

Assignments, tests and quizzes Assignments

Textbooks and References

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Textbooks

• Contact Mechanics by K. L. Johnson, Cambridge University Press, 1987, ISBN 0-521-34796-3

References

• Computational Contact Mechanics:
  • 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
• 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
• 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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