Impact problems have countless applications across physics, technology and life science, ranging from the dynamics of particulate systems like grain or planetary rings over sports to damage and testing of technological or biological materials.

The history of rigorously solved contact-impact problems started together with the history of contact mechanics in the same classical publication by Heinrich Hertz. Looking back, that is not too surprising as the most important “ingredient” to the impact solution is the correct description of the contact mechanical interaction between the colliding bodies, including phenomena like friction, adhesion, dissipative heating, viscoelasticity, plasticity, wear and cracking. Thereby solution of a dynamic contact problem as part in the analysis of impact remains a complex mathematical task.

Due to the variety of applications and the complexity of the contact interaction, collision problems are sometimes treated with insufficient care by specialists of other disciplines, unfamiliar with the possible subtleties of impact mechanics. These subtleties are effectively covered by the method of dimensionality reduction (MDR), a powerful tool developed at our department for the fast simulation of dynamic frictional contacts. Based on MDR, we have been able to comprehensively study collision problems occurring under various different circumstances. Moreover, our approach to the mechanics of impact principally allows the development of effective real time diagnostics and control systems.

The open-access book "Stoßprobleme in Physik, Technik und Medizin - Grundlagen und Anwendungen" aims to build a bridge between tribological theory and applicants of impact problems in other disciplines through the unified presentation of the steps from contact mechanics to the actual impact problem.

Willert, E.: Stoßprobleme in Physik, Technik und Medizin - Grundlagen und Anwendungen. Springer Verlag, Berlin; in press, expected date of publication: January 2020

https://www.springer.com/de/book/9783662602959

Lyashenko, I.A., Popov, V.L.: Impact of an elastic sphere with an elastic half space revisited: Numerical analysis based on the method of dimensionality reduction, Scientific Reports 5, 8479 (2015)

https://www.nature.com/articles/srep08479

Willert, E.; Popov, V.L.: The oblique impact of a rigid sphere on a power-law graded elastic half-space. Mechanics of Materials, 109, 82–87 (2017)

https://www.sciencedirect.com/science/article/pii/S0167663616305713?via%3Dihub

Willert, E.; Kusche, S.; Popov, V.L.: The influence if viscoelasticity on velocity-dependent restitutions in the oblique impact of spheres. Facta Universitatis, Series: Mechanical Engineering, 15(2), 269–284 (2017)

http://casopisi.junis.ni.ac.rs/index.php/FUMechEng/article/view/2797