Computational Contact Mechanics
Welcome to this learning project about computational contact mechanics!
Introduction
editComputational 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
editEducational level: this is a tertiary (university) resource. 
Subject classification: this is an engineering resource. 
 Suggested Prerequisites:
 Time investment: 6 months
 Portal: Engineering and Technology
 School: Engineering
 Department: Mechanical engineering
 Level: Senior year undergraduate and graduate students
Content summary
editThis 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
editThis 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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Textbooks and References
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Textbooks
edit 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, ISBN13 9788895176000.
 Computational Contact Mechanics by P. Wriggers, Springer, 2002, ISBN13 9783540326083
 Computational Contact and Impact Mechanics by T. A. Laursen, Springer, 2002, ISBN13 9783662048641
 Contact Mechanics and Friction. Physical Principles and applications by V.L. Popov, 2nd Edition, Springer, 2017, Chapter 19,
Physical Principles and Applications
editReferences
edit 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:
 KJ. Bathe (1996), Finite Element Procedures, PrenticeHall
 J. N. Reddy (1993), An Introduction to the Finite Element Method, McGrawHill
 O. C. Zienkiewicz and R. L. Taylor (2000), The Finite Element Method: Volume 2 Solid Mechanics, ButterworthHeinemann
 S. C. Brenner and L. R. Scott (2007), The mathematical theory of finite element methods, vol. 15 of Texts in Applied Mathematics, SpringerVerlag
 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/s4054401701773
 BEM for Functionally Graded Materials: Li, Q. & Popov, V.L. Boundary element method for normal nonadhesive and adhesive contacts of powerlaw graded elastic materialsComput Mech (2017). https://doi.org/10.1007/s0046601714619
 Continuum Mechanics:
 A.J.M Spencer (2004), Continuum Mechanics, Dover Publications.
 L.E. Malvern (1969), Introduction to the Mechanics of a Continuous Medium, PrenticeHall
 Mathematics:
 B. Daya Reddy (1998), Introductory Functional Analysis: With applications to boundary value problems and finite elements. , SpringerVerlag