SMALL DEFORMATIONS OF A PLASTIC-RIGID BODY AT THE YIELD POINT

Abstract

An investigation was made of plastic-rigid bodies at the yield point. The boundary conditions were assumed to be such that every element of the material was in the plastic state, and the surface tractions were assumed to vary so that further distortion took place in a quasi-static manner. A perturbation scheme was developed to obtain equations governing Lagrangian stress and velocity increments of the subsequent qausi-static motion. A system of 9 linear equations in 9 unknowns was derived. For the case of plane strain, the system of equations reduced to 3 independent equations in 3 unknown stress increments. By considering the boundary conditions, an expression was derived which related the surface-traction increments with the increments of the stresses. Examples of the compression of a block between rough plates and a thick-walled tube under internal pressure were worked out. In the first case, the theoretical analysis agreed with the published experimental results. In the second example, the minimum rate of strain-hardening necessary to prevent collapse was found.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1953
Accession Number
AD0013810

Entities

People

  • E. T. Onat

Organizations

  • Brown University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Cartesian Coordinates
  • Collapse
  • Compression
  • Equations
  • Hardening
  • Internal Pressure
  • Materials
  • Mathematics
  • Mechanics
  • Strain Hardening
  • Stratified Fluids
  • Stress Strain Relations
  • Stresses
  • Tensor Analysis
  • Yield Strength

Fields of Study

  • Engineering

Readers

  • Fluid Dynamics.
  • Mechanical Engineering/Mechanics of Materials.