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Nucleation, Kinetics and Admissibility Criteria for Propagating Phase Boundaries

  • Rohan Abeyaratne
  • James K. Knowles
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 52)

Abstract

This paper reviews our recent studies on the nucleation and kinetics of propagating phase boundaries in an elastic bar and relates them to various admissibility criteria. First, we discuss how the field equations and jump conditions of the quasi-static theory of such a bar must be supplemented with additional constitutive information pertaining to the initiation and evolution of phase boundaries. The kinetic relation relates the driving traction f at a phase boundary to the phase boundary velocity ; thus f = φ (), where φ is a materially-determined function. The nucleation criterion specifies a critical value of f at an incipient phase boundary. We then incorporate inertial effects, and we find in the context of the Riemann problem that, as long as phase boundary velocities are subsonic, the theory again needs — and has room for — a nucleation criterion and a kinetic relation. Finally, we describe the sense in which each of three widely studied admissibility criteria for phase boundaries is equivalent to a specific kinetic relation of the form f = φ () for a particular choice of φ A kinetic relation based on thermal activation theory is also discussed.

Keywords

Phase Boundary Riemann Problem Jump Condition Entropy Inequality Maxwell Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Rohan Abeyaratne
    • 1
  • James K. Knowles
    • 2
  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

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