Adhesive tangential impact without slip of a rigid sphere and a power-law graded elastic half-space: Numerical analysis based on the Method of Dimensionality Reduction

E. Willert, V. L. Popov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The JKR-adhesive impact of a rigid sphere on a power-law graded half space is studied analytically and numerically under the assumptions of elastic similarity, no-slip and quasi-stationarity. The coefficient of normal restitution is determined analytically. The tangential problem is solved by a numerical algorithm based on the Method of Dimensionality Reduction. The tangential coefficient of restitution is depending on only two properly chosen dimensionless parameters. Thereby the presence of only very weak adhesion severely changes the tangential restitution of the sphere.

Original languageEnglish
Pages (from-to)872-878
Number of pages7
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume97
Issue number7
DOIs
Publication statusPublished - 1 Jul 2017

Fingerprint

Adhesives
Dimensionality Reduction
Slip
Half-space
Numerical analysis
Numerical Analysis
Power Law
Coefficient of restitution
Stationarity
Adhesion
Dimensionless
Numerical Algorithms
Coefficient
Similarity

Keywords

  • JKR-theory
  • Method of Dimensionality Reduction
  • no-slip
  • Oblique elastic impacts
  • power-law graded elastic half-space

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

Cite this

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AB - The JKR-adhesive impact of a rigid sphere on a power-law graded half space is studied analytically and numerically under the assumptions of elastic similarity, no-slip and quasi-stationarity. The coefficient of normal restitution is determined analytically. The tangential problem is solved by a numerical algorithm based on the Method of Dimensionality Reduction. The tangential coefficient of restitution is depending on only two properly chosen dimensionless parameters. Thereby the presence of only very weak adhesion severely changes the tangential restitution of the sphere.

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