Rebound indentation problem for a viscoelastic half‐space and axisymmetric indenter — Solution by the method of dimensionality reduction. Issue 8 (4th November 2015)

• Record Type: Journal Article
• Authors: Argatov, Ivan I.; Popov, Valentin L.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 96:Issue 8(2016)
• Page Start: 956
• Page End: 967
• Publication Date: 2015-11-04
• Subjects: Viscoelastic half‐space -- contact problem -- method of dimensionality reduction; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201500144
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract : The method of dimensionality reduction (MDR) is extended to the axisymmetric frictionless unilateral Hertz‐type contact problem for a viscoelastic half‐space and an arbitrary axisymmetric rigid indenter under the assumption that the circular contact area (arbitrarily evolving in time) remains singly connected during the whole process of indentation. In particular, the MDR is applied to study in detail the so‐called rebound indentation problem, where the contact radius has a single maximum. It is shown that the obtained closed‐form analytical solution for the rebound indentation displacement (recorded in the recovery phase, when the contact force vanishes) does not depend on the indenter shape. Abstract : The method of dimensionality reduction (MDR) is extended to the axisymmetric frictionless unilateral Hertz‐type contact problem for a viscoelastic half‐space and an arbitrary axisymmetric rigid indenter under the assumption that the circular contact area (arbitrarily evolving in time) remains singly connected during the whole process of indentation. In particular, the MDR is applied to study in detail the so‐called rebound indentation problem, where the contact radius has a single maximum. It is shown that the obtained closed‐form analytical solution for the rebound indentation displacement (recorded in the recovery phase, when the contact force vanishes) does not depend on the indenter shape.