Indentation over a transversely isotropic, poroelastic, and layered half-space

Zhiqing Zhang, Ernian Pan*, Jiangcun Zhou, Chih Ping Lin, Shuangbiao Liu, Qian Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Poroelastic materials are common in nature and have applications in many engineering fields. In this paper, we derive a general solution of indentation over a multilayered half-space consisting of transversely isotropic and poroelastic materials. The rigid disc-shaped indenter is subjected to a vertical force of Heaviside time-variation. The solution is expressed in terms of the recently introduced powerful Fourier-Bessel series (FBS) system of vector functions combined with the unconditionally stable dual-variable and position method for dealing with layering. Since the problem is a mixed boundary-value one, the Green's functions due to a vertical ring-load are first derived which are then utilized in the integral least-square formulation to derive the solution. In terms of the FBS method, the expansion coefficients, which are further called Love numbers, are discrete, and therefore can be pre-calculated and used repeatedly for different field points on the surface. As such, the solution based on the new FBS method is more efficient and accurate than previous integral-transform methods. This new FBS method is particularly attractive when dealing with mixed boundary-value problems where time-variation is further involved. Numerical examples are conducted to validate the accuracy of the proposed solution and to demonstrate the effects of material layering, geometry, and hydraulic boundary conditions on the contact performance of the material system.

Original languageEnglish (US)
Pages (from-to)588-606
Number of pages19
JournalApplied Mathematical Modelling
StatePublished - Mar 2024


  • Consolidation
  • Dual-variable and position method
  • FBS system of vector functions
  • Layered poroelasticity
  • Love number
  • Transverse isotropy

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


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