A Functional Equation Governing Moving Phase Boundaries in an Elastic Bar.

Abstract

Certain elastic solids when subjected to sufficiently high loads abruptly change their mechanical properties and yet continue to respond elastically to further loading. In one dimension such mechanically induced elastic phase transitions may be due to a non-monotonic stress-strain curve. This document investigates the cumulative reflection of acoustic waves between the external boundary of the solid and the internal moving boundary separating distinct elastic phases. This latter phase boundary is similar to a gas dynamical shock wave. For the material introduced in this work, a functional equation governing the trajectory of a phase boundary is derived and shown to have a unique solution. This equation is treated asymptotically to determine the large time behavior of the phase boundary. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA158178

Entities

People

  • T. J. Pence

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustic Waves
  • Equations
  • Materials
  • Mathematics
  • Mechanical Properties
  • Mechanics
  • Phase
  • Phase Transformations
  • Shock
  • Shock Waves
  • Stress Strain Relations
  • Stresses
  • Theorems
  • Trajectories
  • Transitions
  • United States
  • Waves

Fields of Study

  • Mathematics

Readers

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