Response of Polymers to Tensile Impact. 2. Extension of the Integral-Equation, Successive-Substitution Solution to Non-Linear, Time-Independent Materials

Abstract

An integral-equation, successive- substitution solution for the propagation of strain waves in a linear elastic material, developed in an earlier paper, is here extended to non-linear materials without creep (time-independent materials). A PREVIOUSLY-PUBLISHED PROBLEM, BASED ON EXPERIMENTAL DATA FOR NYLON STRING IS SOLVED BY THE SUCCESSIVE-SUBSTITUTION METHOD AND COMPARED WITH THE EARLIER SOLUTION OBTAINED BY THE METHOD OF CHARACTERISTICS. The agreement of the two solutions is at first good, but in the region where the stress-strain curve of the nylon is concave upward a tendency to oscillation builds up and the solution eventually oscillates. This occurs in approximately the same region where shock waves can appear in a method-of-characteristics solution. Oscillations in the strained portion of a string are examined theoretically and it is shown that the energy of standing waves can be used to obtain energy conservation. Although the successive-substitution method generates oscillations when it has to deal with a discontinuity in strain, the possibility that oscillations also actually exist as a means of conserving energy cannot be ruled out.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1974
Accession Number
AD0780811

Entities

People

  • Harold J. Hoge
  • Malcolm N. Pilsworth Jr.
  • Prescott D. Crout

Organizations

  • United States Army Soldier Systems Center

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Computational Science
  • Differential Equations
  • Digital Computers
  • Discontinuities
  • Equations
  • Experimental Data
  • Integral Equations
  • Materials
  • Mathematical Analysis
  • Mechanics
  • Method Of Characteristics
  • Military Research
  • Numerical Analysis
  • Shock Waves
  • Standing Waves
  • Stress Strain Relations
  • Waves

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.