Summary
A dynamical phenomenon in one-dimensional materials with internal state variables is investigated. It is shown that there can exist stationary singular points at which the second spatial derivative of the deformation and the spatial derivatives of the internal state variables are discontinuous. Explicit expressions for the variation of the discontinuities are derived. For the material with an unknown number of internal state variables, a lower bound for the number can be obtained by observing the behaviour of the discontinuity of the second spatial derivative of the deformation at a stationary singular point.
Zusammenfassung
Es wird ein dynamisches Phänomen in eindimensionalen Materialien mit internen Zustandsvariablen behandelt. Es wird gezeigt, daß stationäre Singularitäten auftreten können, bei welchen die zweite Ortsableitung der Verformung und die Ortsableitungen der internen Zustandsvariablen unstetig sind. Explizite Ausdrücke für die Variation der Unstetigkeiten werden hergeleitet. Für ein Material mit einer unbekannten Anzahl interner Zustandsvariablen kann eine untere Schranke für die Anzahl durch Beobachtung der Unstetigkeiten der zweiten Ortsableitung der Verformung an der Stelle der stationären Singularität erhalten werden.
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Matsumoto, E. Behaviour of the stationary singular points in one-dimensional materials with internal state variables. Acta Mechanica 39, 241–249 (1981). https://doi.org/10.1007/BF01170345
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DOI: https://doi.org/10.1007/BF01170345