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On the application of fracture mechanics mixed-mode models of sliding with friction and adhesion --- the Menga, Carbone & Dini paradox

Mike Ciavarella's picture

I attach a PREPRINT of a paper on the Menga, Carbone & Dini paradox (published in JMPS last year, available at https://arxiv.org/pdf/1710.06506.pdf), that is on the application of thermodynamics to mixed mode fracture mechanics models of contacts with friction and adhesion, and an apparent paradox which emerges from this treatment.  Comments welcome.   

 I also attach a simpler direct energetic formulation (see menga-maugis.pdf attached) which has completely different, and more reasonable, results.  What goes wrong with the Legendre transform formulation?

 See also https://www.tribonet.org/should-the-contact-area-really-increase-due-to-sliding-and-why-this-is-never-observed/  

 Keywords: Adhesion, JKR model, friction, soft matter, fracture mechanics, mixed mode, cohesive models.

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PDF icon menga-view.pdf117.82 KB
PDF icon 1908.04490.pdf139 KB

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Mike Ciavarella's picture

Please find attached in the main post some further notes about the paradox, with possible reasons why the paradox emerged.

Mike Ciavarella's picture

 

 I also attach a simpler direct energetic formulation (see menga-maugis.pdf attached) which has completely different, and reasonable, results, in line with the classical theories and the experiments.  What goes wrong with the Legendre transform formulation?

Mike Ciavarella's picture

https://arxiv.org/pdf/1908.04490.pdf 

We offer a possible solution to the paradox 

Comments welcome, as double checking is mandatory on such completely opposite conclusions to avoid embarrassing situations for both authors and editors...

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