January 12, 2015 at 7:54 am #3174
Dear nanofriends, it is my great pleasure and honor to present to you the English edition of the book „Method of Dimensionality Reduction in Contact Mechanics and Friction“, (Springer, formal copyright 2015, but appeared already in September 2014).
If you are interested in the book and would like to make your own opinion about the MDR, just send me an e-mail to: email@example.com and I will send you the complete electronic version of the book.
The book contains description of the method of dimensionality reduction (MDR), its applications as well as all necessary proofs (Chapters 17,18 and 19). It also describes in detail the area of applicability of the MDR – already in the Introduction to the book and at other suitable places.
The book appeared originally in German in 2013:
If you prefer to have the German edition, please let me know, and I will send you electronic version of the German edition.
Other relevant publications on MDR with short comments (including the critical comment of Persson in PRL and our reply to it) can be found and downloaded here:
The main part of the MDR is not new and goes back to the works of Galin (and independently Green and Collins). MDR just formulates this method in the form of a simple and universal tool and generalizes it to contacts of viscoelastic materials using the theorems of Li and Radok, to tangential contacts using the superposition principles of Jäger (as well as earlier works by Cattaneo and Mindlin) and to adhesive contacts using the work of Heß. Further, it was generalized and verified for non-axially symmetric contacts as e.g. randomly rough surfaces by comparison with direct three-dimensional BEM simulations, see dissertation of R. Pohrt, TU Berlin, 2013 (in this case, the MDR is approximate and applies not to all properties!)
The above contact mechanical theories – after summarizing them in the form of the MDR – become so simple that I now teach them even for students of the first semester which just begin to study mechanics of materials. The whole contact mechanics in the MDR formulation is not more complicated that the classical beam theory and is really suitable even for young people who just learned the basics of integration and differentiation.
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