Contacts with limited interpenetration

0558123 - MÚ 2023 RIV NL eng J - Journal Article
Jarušek, Jiří
Contacts with limited interpenetration.
MethodsX. Roč. 9, April (2022), č. článku 101688. E-ISSN 2215-0161
Institutional support: RVO:67985840
Keywords : approximate problems * contact with limited interpenetration * coulomb friction * existence of solutions
OECD category: Pure mathematics
Impact factor: 1.9, year: 2022
Method of publishing: Open access
https://doi.org/10.1016/j.mex.2022.101688

The aim of this paper is to acquaint a wider public of applied mathematicians, numerical analysts and engineers with the model of contact with limited interpenetration as a suitable framework for computation of practical problems. It is mostly based on the newly published Ref. [5]. The model is physically well based on the microscopic structure of a standard material of a body being in an actual or potential contact with a rigid foundation. Such microscopic phenomena are macroscopically interpreted as a certain but strictly limited surface interpenetration of both objects. The essence of this interpenetration is depicted in the graphical abstract. After a brief description of its motivation and the method itself, a comparison with the other contact models available together with the detailed description of the graphical abstract is presented. Furthermore, the application of the method to a quasistatic frictional boundary contact is described. Moreover, a brief description of the methods used in the proof of the existence of solutions of such contact problems is provided. If the depth of the interpenetration tends to zero, then there is some sequence of solutions of such problems and some solution to the corresponding Signorini contact problem such that it is the limit of the sequence. Requirements for the use of the presented model in solving practical problems as well as its other aspects are briefly discussed. Summing up: • the presented and other results published (Refs. [1–4]) create a reliable basis of the numerical analysis of the problems, • the method is ready to be used in solving a wide class of contact problems arising in technical practice.
Permanent Link: http://hdl.handle.net/11104/0331927