### Abstract

The low-velocity oblique impact of a rigid sphere on a power-law graded elastic half-space is studied under the assumptions of elastic similarity and a constant coefficient of friction. The normal component of motion is determined analytically. The tangential problem is investigated numerically using the Method of Dimensionality Reduction. We find that the solution of the impact problem written in proper dimensionless variables is the same as in the homogeneous case. This solution therefore can possibly be generalised for arbitrary inhomogeneous material behaviour, if the Mindlin ratio has no spatial dependence. However, different physical ranges are possible for the dimensionless variables in the homogenenous and inhomogeneous cases, which is why, in the case of power-law grading, parameter combinations are possible, for which no kinetic energy is dissipated during the impact. The maximum contact pressures during normal impact can be significantly reduced by the usage of power-law grading.

Original language | English |
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Pages (from-to) | 82-87 |

Number of pages | 6 |

Journal | Mechanics of Materials |

Volume | 109 |

DOIs | |

Publication status | Published - 1 Jun 2017 |

### Fingerprint

### Keywords

- Friction
- Method of dimensionality reduction
- Oblique elastic impacts
- Power-law-graded elastic half-space

### ASJC Scopus subject areas

- Materials Science(all)
- Instrumentation
- Mechanics of Materials

### Cite this

**The oblique impact of a rigid sphere on a power-law graded elastic half-space.** / Willert, E.; Popov, V. L.

Research output: Contribution to journal › Article

*Mechanics of Materials*, vol. 109, pp. 82-87. https://doi.org/10.1016/j.mechmat.2017.03.019

}

TY - JOUR

T1 - The oblique impact of a rigid sphere on a power-law graded elastic half-space

AU - Willert, E.

AU - Popov, V. L.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - The low-velocity oblique impact of a rigid sphere on a power-law graded elastic half-space is studied under the assumptions of elastic similarity and a constant coefficient of friction. The normal component of motion is determined analytically. The tangential problem is investigated numerically using the Method of Dimensionality Reduction. We find that the solution of the impact problem written in proper dimensionless variables is the same as in the homogeneous case. This solution therefore can possibly be generalised for arbitrary inhomogeneous material behaviour, if the Mindlin ratio has no spatial dependence. However, different physical ranges are possible for the dimensionless variables in the homogenenous and inhomogeneous cases, which is why, in the case of power-law grading, parameter combinations are possible, for which no kinetic energy is dissipated during the impact. The maximum contact pressures during normal impact can be significantly reduced by the usage of power-law grading.

AB - The low-velocity oblique impact of a rigid sphere on a power-law graded elastic half-space is studied under the assumptions of elastic similarity and a constant coefficient of friction. The normal component of motion is determined analytically. The tangential problem is investigated numerically using the Method of Dimensionality Reduction. We find that the solution of the impact problem written in proper dimensionless variables is the same as in the homogeneous case. This solution therefore can possibly be generalised for arbitrary inhomogeneous material behaviour, if the Mindlin ratio has no spatial dependence. However, different physical ranges are possible for the dimensionless variables in the homogenenous and inhomogeneous cases, which is why, in the case of power-law grading, parameter combinations are possible, for which no kinetic energy is dissipated during the impact. The maximum contact pressures during normal impact can be significantly reduced by the usage of power-law grading.

KW - Friction

KW - Method of dimensionality reduction

KW - Oblique elastic impacts

KW - Power-law-graded elastic half-space

UR - http://www.scopus.com/inward/record.url?scp=85017169774&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017169774&partnerID=8YFLogxK

U2 - 10.1016/j.mechmat.2017.03.019

DO - 10.1016/j.mechmat.2017.03.019

M3 - Article

VL - 109

SP - 82

EP - 87

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

ER -