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.
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