Abstract
The instability of an initially compressed half-space which consists of dilatant frictional materials is examined. It is assumed that the material response is governed by elastoplastic constitutive relations that include plastic compressibility (or dilatancy) and frictional effects, and hence involves a nonassociative flow rule. Stability limits are established, and it is shown that (unlike for elastic materials) for this class of materials folding by surface instability can be initiated at compressive forces that are considerably smaller than the initial shear modulus. The results are illustrated in terms of some published data on certain sandstones.
Zusammenfassung
Die Instabilität eines zusammengedrückten Halbraumes aus kompressiblem Material mit Reibung wird untersucht. Das Material soll elastisch plastischen Stoffgleichungen mit plastischer Kompressibilität und Reibungseffekten genügen. Die Fließregel ist demzufolge nicht jene des plastischen Potentials. Die Stabilitätsgrenzen sind aufgeteilt, und es wird gezeigt, daß im Gegensatz zu elastischen Materialien die Deformation infolge der Oberflächeninstabilität für das vorliegende Stoffverhalten schon bei Druckspannungen entsteht, welche im Vergleich zum Anfangswert des Schubmodulus viel kleiner sind. Die Resultate sind mit Hilfe von bereits publizierten Kennwerten von gewissen Sandsteinen numerisch ausgewertet.
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Horii, H., Nemat-Nasser, S. Instability of a half-space with frictional materials. Z. angew. Math. Phys. 33, 1–16 (1982). https://doi.org/10.1007/BF00948308
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DOI: https://doi.org/10.1007/BF00948308