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Strength of adhesive contacts: Influence of contact geometry and material gradients


The strength of an adhesive contact between two bodies can strongly depend on the macroscopic and microscopic shape of the surfaces. In the past, the influence of roughness has been investigated thoroughly. However, even in the presence of perfectly smooth surfaces, geometry can come into play in form of the macroscopic shape of the contacting region. Here we present numerical and experimental results for contacts of rigid punches with flat but oddly shaped face contacting a soft, adhesive counterpart. When it is carefully pulled off, we find that in contrast to circular shapes, detachment occurs not instantaneously but detachment fronts start at pointed corners and travel inwards, until the final configuration is reached which for macroscopically isotropic shapes is almost circular. For elongated indenters, the final shape resembles the original one with rounded corners. We describe the influence of the shape of the stamp both experimentally and numerically.

Numerical simulations are performed using a new formulation of the boundary element method for simulation of adhesive contacts suggested by Pohrt and Popov. It is based on a local, mesh dependent detachment criterion which is derived from the Griffith principle of balance of released elastic energy and the work of adhesion. The validation of the suggested method is made both by comparison with known analytical solutions and with experiments. The method is applied for simulating the detachment of flat-ended indenters with square, triangle or rectangular shape of cross-section as well as shapes with various kinds of faults and to “brushes”. The method is extended for describing power-law gradient media.


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Authors acknowledge the aßsistance of C. Jahnke in conduction of experiments and very useful discussions of adhesion with gradient media with M. Heß and E. Willert. This work has been conducted under partial financial support from DFG (Grant number PO 810/22-1).

Contributions of authors: R. Pohrt built the experimental setup and processed the experimental data. R. Pohrt and Q. Li executed the numerical simulations. Theoretical analysis was carried our primarily by V. L. Popov. All authors contributed equally to the writing of the manuscript.

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Correspondence to Valentin L. Popov.

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Valentin L. POPOV. He is full professor at the Berlin University of Technology. He studied physics and obtained his doctorate in 1985 from the Moscow State Lomonosov University. 1985–1998 he worked at the Institute of Strength Physics and Materials Science of the Russian Academy of Sciences and was a guest professor in the field of theoretical physics at the University of Paderborn (Germany) from 1999 to 2002. Since 2002 he is the head of the Department of System Dynamics and the Physics of Friction at the Berlin University of Technology. He has published over 300 papers in leading international journals and is the author of the book “Contact Mechanics and Friction: Physical principles and applications” which appeared in three editions in German, English, Chinese, and Russian. He is the member of editorial boards of many international journals and is organizer of more than 20 international conferences and workshops over diverse tribological themes. Prof. Popov is Honorary Professor of the Tomsk Polytechnic University, of the East China University of Science and Technology, and of the Changchun University of Science and Technology and Distinguished Guest Professor of the Tsinghua University. His areas of interest include tribology, nanotribology, tribology at low temperatures, biotribology, the influence of friction through ultrasound, numerical simulation of contact and friction, research regarding earthquakes, as well as topics related to materials science such as the mechanics of elastoplastic media with microstructures, strength of metals and alloys, and shape memory alloys.

Roman POHRT. He is independent researcher at the Berlin University of Technology. He studied physical engineering science with special focus on simulation and optimization of discrete and continuous problems. Since he joined the group of Prof. V. Popov in 2010, he has been conducting experimental and numerical research on a variety of tribology related industry problems. In his PhD thesis R. Pohrt focussed on linking scales in the elastic contact of fractal rough surfaces, for which he was awarded by the German Tribological Society in 2013. R. Pohrt has authored a series of influential papers on different tribological problems, applying and extending state-of-the-art numerical methods. His areas of interest include contact mechanics, rail-wheel-interaction of trains, manufacturing technology, and lubrication and more generally the influence of surface topography on tribological phenomena.

Qiang LI. He is a postdoctoral researcher at the Berlin University of Technology. He studied mechanical engineering in East China University of Science and Technology. He obtained his doctorate at the Berlin University of Technology in 2014 and now works as a scientific researcher at the Department of System Dynamics and the Physics of Friction headed by Prof. V. L. Popov. He has published over 20 papers in international journals including Physical Review Letters. His scientific interests include tribology, elastomer friction, hydrodynamic lubricated contact, numerical simulation of frictional behaviors, and fast numerical method based on boundary element method.

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Popov, V.L., Pohrt, R. & Li, Q. Strength of adhesive contacts: Influence of contact geometry and material gradients. Friction 5, 308–325 (2017).

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  • adhesion
  • boundary element method (BEM)
  • flat-ended indenters
  • gradient media