Young's modulus interpreted from plane compressions of geomaterials between rough end blocks

Kam Tim Chau

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

This note derives an approximate expression of the true Young's modulus of a rectangular solid under plane compression between two rough end blocks, provided that the Poisson's ratio ν of the solid is known. The friction between the loading platens and the ends of the specimen is assumed to be large enough to restrain slippage at the contact. By using the function space concept of Prager and Synge (1947), a correction factor λ with calculable error is obtained which can be multiplied to the apparent Young's modulus (i.e., the one obtained by assuming uniform stress field) to yield the true Young's modulus; it is evaluated numerically for 0 ≤ ν ≤ 0.49 and 0 ≤ η ≤ 3 (where η = b/h with b and h being the half width and half length of the specimen). In general, λ increases with ν and η for both plane strain and plane stress compressions. Within this range of ν and η, λ may vary from 0.37-1.0 for the plane strain case and from 0.84-1.0 for the plane stress case. Thus, the assumption of uniform stress field may lead to erroneous interpretation of the Young's modulus. When the special case of ν = 1/3 and η = 1 is considered, we obtain λ = 0.9356, which compares well with 0.9359 obtained by Greenberg and Truell (1948).
Original languageEnglish
Pages (from-to)4963-4974
Number of pages12
JournalInternational Journal of Solids and Structures
Volume36
Issue number31-32
DOIs
Publication statusPublished - 1 Jul 1999

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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