The Boussinesq flat-punch indentation problem within the context of linearized viscoelasticity

Hiromichi Itou, Victor A. Kovtunenko*, Kumbakonam R. Rajagopal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Boussinesq problem, namely the indentation of a flat-ended cylindrical punch into a viscoelastic half-space is studied. We assume a linear viscoelastic model wherein the linearized strain is expressed as a function of the stress. However, this expression is not invertible, which makes the problem very interesting. Based on the Papkovich–Neuber representation in potential theory and using the Fourier–Bessel transform for axisymmetric bodies, an analytical solution of the resulting time-dependent integral equation is constructed. Consequently, distribution of the displacement and the stress fields in the half space with respect to time is obtained in the closed form.

Original languageEnglish
Article number103272
JournalInternational journal of engineering science
Publication statusPublished - Jun 2020


  • Axisymmetric body
  • Boussinesq problem
  • Closed form solution
  • Fourier–Bessel transform
  • Implicit material response
  • Linear viscoelasticity
  • Papkovich–Neuber representation
  • Potential theory
  • Punch indentation

ASJC Scopus subject areas

  • Materials Science(all)
  • Engineering(all)
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'The Boussinesq flat-punch indentation problem within the context of linearized viscoelasticity'. Together they form a unique fingerprint.

Cite this