Dynamic contact problem with moderate displacement and time‐dependent normal

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 102; no. 12
• Main Author: Wu, Shen R.
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.12.2022
• Subjects: Dependent variables; Displacement; Time dependence
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.202100451

In the publications on existence of solutions to the dynamic contact problems, small displacement was basically assumed. To extend the qualitative study for more general applications with moderate displacement and general shape of surfaces, the normal of contact surface is treated as time‐dependent variable in the contact mechanics model. The frictional dynamic contact problem with unilateral constraint is formulated in a variational inequality. The penalized variational equation is derived with two penalty terms, verifying contact condition and applying constraint on the normal velocity, respectively. For given penalty parameter the penalized variational equation is proved to have solution, which converges to the solution of the variational inequality. The true contact boundary, varying in time, is determined in the process and the constraint condition is satisfied. The regularity of the solution is similar to the results by others under the assumption of small displacement. In the publications on existence of solutions to the dynamic contact problems, small displacement was basically assumed. To extend the qualitative study for more general applications with moderate displacement and general shape of surfaces, the normal of contact surface is treated as time‐dependent variable in the contact mechanics model. The frictional dynamic contact problem with unilateral constraint is formulated in a variational inequality.…