Transient and steady-state viscoelastic contact responses of layer-substrate systems with interfacial imperfections

Xin Zhang, Q. Jane Wang*, Tao He

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


This paper reports the development of a novel semi-analytical model for solving the transient and steady-state contact responses of a rigid sphere sliding/rolling on a viscoelastic layer-elastic substrate system. The displacement transmissions at the layer-substrate interface are affected by spring-like or dislocation-like defects. The analytical transient and steady-state viscoelastic frequency response functions (FRFs) are derived from the elastic solutions with imperfect interfaces. Instead of using the integration form of the creep function, viscoelastic modulus Ε(ω) is directly incorporated into the viscoelastic FRFs by a frequency-velocity transform that links the time-related frequency, ω, and sliding velocity, V, with the space-related frequency number, m, i.e. ω=−mV. The solutions are so formulated that fast numerical techniques, such as the conjugate gradient method (CGM) and the discrete convolution-fast Fourier transform (DC-FFT) algorithm, can be incorporated for computation efficiency. The developed model is employed to investigate the effects of layer thickness, modulus, sliding velocity, and the degree of interface imperfection on the viscoelastic contact response of the material system, including pressure distributions, displacements, viscoelastic dissipation, and subsurface stresses.

Original languageEnglish (US)
Article number104170
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Dec 2020


  • Imperfect interface
  • Layered system
  • Steady-state
  • Transient
  • Viscoelastic contact

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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