Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems

Zhanjiang Wang*, Hao Yu, Qian Wang

*Corresponding author for this work

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

This paper reports the derivation of the explicit integral kernels for the elastic fields due to eigenstrains in two joined and perfectly bonded half-space solids or bimaterials. The domain integrations of these kernels result in the analytical solutions to displacements and stresses. When the eigenstrains are all in solid I, the kernel for the elastic fields has four groups in this solid and two groups in the other joined solid. Explicit closed-form solutions for a cuboidal inclusion with uniform eigenstrains are derived as the basic solutions, i.e., the influence coefficients. When the computational domain is meshed into cuboidal elements of the same sizes, the total elastic fields can be quickly obtained by implementing three-dimensional fast Fourier transform-based algorithms. The results for the fields due to a cuboidal, a spherical, and a cylindrical inclusion, as well as multiple cuboidal inclusions are presented and discussed. Residual stresses in an elasto-plastic contact involved a coated substrate is further analyzed with the new solution approach.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalInternational journal of plasticity
Volume76
DOIs
StatePublished - Aug 17 2016

Keywords

  • A. Inclusions
  • Analytical solutions
  • B. Layered material
  • Fast Fourier transform (FFT)
  • Joined half-spaces

ASJC Scopus subject areas

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

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