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Lecture notes or material to get start Contact Mechanics.


I am a Phd student. My Area of work is the study of contact-impact mechanics problems using newly developed Isogeometric analysis method. I have tried to learn the methodology used to solve the simple (I mean elastic, frictionless or frictional, non-adhesive and smooth surface) contact-impact problems  with the help of most popular books (a few chapters or some portion of books written by Zhi Hua Zhong (Finite element analysis of contact-impact problem), Peeter Wriggers (Computational Contact Mechanics) etc. ) and papers providing the formulation of problems. But I think I couldn't grasp the methodology provided in the books or papers, therefore I am looking for numerical procedure and implementation algorithms (codes may also be helpful) of simple one- and two-dimensioanl contact problmes. May be my understanding will be more clear if I undertand the theory with the complete (step-by-step) numerical procedure to solve a contact problem. Therefore, I will be highly obliged of your if you could help me to suggest the way of learning. If my way of learning this subject is completely wrong, please let me this too.

Thanks to take the pain.




Vishal Agrawal 


Hi Vishal,

There are many sources in internet explaining contact formulation in Finite elements. For e.g., seems good. It would be better to understand the treatment of contact mechancis given in K.L. Johnson before understanding the FEM version of treating contacts.

By the way, are you working with Dr. Sachin Singh Gautam at IIT Guwahati? I find your topic close to his areas of interest. Anyway, my best wishes for you.

With Regards,


Hi Sir,

Yes, Dr. Sachin Singh Gautam is my Supervisor. I am really glad that you replied but I am unable to find the complete formulation of a particular-kind of problem and its treatment. As in FEM, to solve a plate with a hole problem (for a case), we have 2D stress-strain formulation, available in almost all books. From there any student can learn the way of analysis of such problem. Can't we learn the analysis of contact mechanics problems similar to the FEM..?

Thanks a lot sir,


Vishal Agrawal 

Hi Vishal,

Convey my wishes to your supervisor. We know each other pretty well.

Coming to your question on contact-impact formulations, I never implemented contact in FEM codes. But, I read and understood the concept to some extent from the paper by Camacho and Ortiz. It is based on predictor-corrector type. Here is the link to that paper :

Please have a look at it. If I find anything better I will get back to you.



Sure Sir, 

Your familiarization with my supervisor makes me glad. I will convey your wishes. Thanks for the paper, it seems quite helpful. Currently, my task is to solve a few simple contact-impact problem to understand the physics and theory of this subject practically. 

Thanks again Sir,



Ajay B Harish's picture

Dear Vishal,

You could also check the recent book by Dr. Konyukhov (,subjectCd-M...). I would suggest this & this is meant to be an introductory text for those working in contact mechanics. They do provide codes that can be run with FEAP & could give a more hands-on approach.

Once you have a better grasp of the concepts, you could look at the book "Computational Contact Mechanics" by Peter Wriggers or "Computational Contact & Impact Mechanics" by Tod Laursen. Both of these books are more of an advanced text. 

Best Regards

Dear Sir,

I checked the book by Dr. knoyukhov. It really seems intresting and explains a lot things to a beginner student to Continuum Mechanics subject. But still I feel there are lots and lots of things to cover for me. I've even tried myself with the book "Computational Contact Mechanics", but I couldn't even grasp very little things from there and still I have no clue to solve the simple  problems in this subject as none of them provide the complete solution to a problem.

I've just visited your profile and it is really amazing to know that you are working under respected prof. Peter Wriggers. Therefore, again I would like to go through with book by Dr. Konyukhov as you suggested, may be this time I would be able to catch more things.

Thanks for the help. :)




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