An ingenious work on contact mechanics by Föppl and Schubert went into oblivion due to the Second World War

The history of science sometimes reads like a detective novel. The personal destinies sometimes lead to the fact that outstanding, ingenious works which were decades ahead of their time, sink into oblivion. This seems to have happened with the publications of Föppl (1941) and Schubert (1942) on contact mechanics of plane and axisymmetric bodies. The results obtained by Schubert using the method previously developed by Föppl cover a large amount of results found by dozens of researches during almost half a century. If these two publications became known, contact mechanics would have received a very intensive impetus already in 1941.

The equations obtained by Föppl and Schubert became widely known due to publication by Sneddon in 1965, 24 years after the Föppls publication and it took further decades until it became well-known and “established”.

Neither at the time of the publications by Föppl and Schubert nor at the time of the much later publication by Sneddon, was it noticed that the equations of Föppl-Schubert-Sneddon allow a simple physical interpretation in terms of an effective contact with a linear elastic foundation. This further step was made in the framework of the Method of Dimensionality Reduction, which, according to Barber, is basically a reinterpretation of the equations of Föppl-Schubert-Sneddon using a simple contact with a one-dimensional elastic foundation. Even if not widely known, Föppl and Schubert initiated this process of drastic simplification of contact mechanics, which finally, due to recent developments, became accessible even to students of physics or engineering in the first semester. The parametrization invented by Föppl remains to our day the most simple and elegant method of solving axisymmetric contact problems. It can be strongly recommended to anyone who teaches contact mechanics.

The paper “Ludwig Föppl and Gerhard Schubert: Unknown classics of contact mechanics” contains not only historical background but also a complete English translation of the paper by Schubert “On Stress Distribution under Elastically Mounted Load Bearing Structures”.

This article is based on the abstract and conclusion of the paper: Elena Popova, Valentin L. Popov: Ludwig Föppl and Gerhard Schubert: Unknown classics of contact mechanics, Z Angew Math Mech.2020; 100: e202000203. https://onlinelibrary.wiley.com/doi/full/10.1002/zamm.202000203