Formulas for the Pressure and Bulk Modulus in Uniaxial Strain.

Abstract

For an isotropic elastic solid, the Pressure P = Pu(P) in a state of uniaxial strain at density p generally differs from the pressure P = Ph(p) in a state of hydrostatic stress at the same density. Several researchers have used pressure/shear (or oblique plate impact) tests to determine Pu and the corresponding uniaxial bulk modulus Ku is equivalent to pdPu/dp. The pressur/shear tests yield uniaxial longitudinal and shear moduli, Lu and Gu, as functions of p. A common procedure is to integrate the approximate relation Ku approx. = Lu - 4/3Gu to obtain the pressure-density relation P = Pu(P) in uaiaxial strain. It is shown here that the integration of this approximate relation between the moduli can be avoided altogether by utilizing the exact formula Pu = a1 - 2/3((p/po)2 - 1)Gu, where a1 denotes the longitudinal stress (positive in comPression). The bulk modulus Ku is computed exactly from this formula, and the wor in approximating it by Lu - 4/3Gu is determined. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1996
Accession Number
ADA304036

Entities

People

  • Michael J. Scheidler

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bulk Modulus
  • Commerce
  • Compression
  • Impact Tests
  • Materials
  • Materials Testing
  • Mechanical Properties
  • Military Research
  • Optical Materials
  • Physical Properties
  • Secondary Waves
  • Shear Modulus
  • Shear Stresses
  • Shear Tests
  • Shock Waves
  • Stresses
  • Waves

Readers

  • Mechanical Engineering/Mechanics of Materials.
  • Military History
  • Systems Analysis and Design