Kinetic Relations and the Propagation of Phase Boundaries in Solids

Abstract

This paper investigates the dynamics of phase transformations in elastic bars. The specific issue studied is the compatibility of the field equations and jump conditions of the one-dimensional theory of such bars with two additional constitutive requirements: the first of these is a kinetic relation controlling the rate at which the phase transition takes place; the second is a nucleation criterion for the initiation of the phase transition. A special elastic material with a piecewise-linear, non-monotonic stress-strain relation is considered, and the Riemann problem for this material is analyzed. For a large class of initial data, it is found that the kinetic relation and the nucleation criterion together will single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities. (jhd)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1989
Accession Number
ADA226119

Entities

People

  • James K. Knowles
  • Rohan Abeyaratne

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Cauchy Problem
  • Continuum Mechanics
  • Differential Equations
  • Dynamics
  • Elastic Materials
  • Equations
  • Materials
  • Materials Science
  • Mathematics
  • Mechanical Engineering
  • Mechanics
  • Partial Differential Equations
  • Phase Transformations
  • Physics
  • Shock Waves
  • Stress Strain Relations
  • Transitions

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Materials Science (Mechanical Engineering).