A Functional Equation Governing Moving Phase Boundaries in an Elastic Bar.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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