Contact Problem for a Rigid Punch and an Elastic Half Space as an Inverse Problem

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 240; no. 2; pp. 184 - 193
• Main Authors: Obodan, N. I., Zaitseva, T. A., Fridman, O. D.
• Format: Journal Article
• Language: English
• Published: New York Springer US 04-07-2019; Springer; Springer Nature B.V
• Subjects: Adhesion; Elastic half spaces; Friction; Indentation; Inverse problems; Mathematics; Mathematics and Statistics; Separation
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-019-04346-2

We solve a contact problem of indentation of a punch into an elastic half space with regard for the friction and in the presence of the zones of adhesion, sliding, and separation. The applied approach is based on the statement of the problem in the form of the inverse problem in which the Coulomb law of friction is used as an additional condition in the regions with friction. In the formulation of the inverse problem, we take into account the presence of the zones of adhesion whose sizes are unknown. The correctness of the solution of the inverse problem is analyzed. The proposed approach, in combination with the procedure of discretization, enables us to determine the zones of microsliding alternating with the zones of adhesion and separation.