Abstract
The formulation of a backward difference algorithm based on an internal variable description for piecewise linear yield surfaces is presented. Attention is restricted to an associated flow rule and isotropic material behaviour. The Tresca and Mohr-Coulomb yield surfaces with perfectly plastic and linear hardening rules are considered in detail. The algorithm has the advantages of being fully linked to the governing principles and avoiding the inherent problems associated with corners on the yield surface. It is used to identify return paths in stress space for the Tresca and Mohr-Coulomb yield surfaces with perfectly plastic and linear hardening rules. These return paths provide a basis against which heuristically developed algorithms can be compared.
Sommario
Il lavoro presenta la formulazione di un particolare algoritmo di differenza all'indietro basato su una variabile interna descrittiva di una superficic di snervamento lincare a tratti. L'interesse del lavoro e'ristretto allo studio della legge di evoluzione ed ad un comportamento isotropo del materiale. Vongono csaminate in dettaglio le superfici di snervamento di Tresca e di Mohr-Coulomb per comnportamento perfettemente plastico ed incrudimento lineare. L'algoritmo presenita il vantaggio di essere completamente integrato nella formulazione ed evita quei problemi connessi con una descrizione della superficie di snervamento spigolosa. Esso e' usato per identificare, nello spazio delle tensioni, il cammino di ritorno per superfici di snervamento alla Tresca e Mohr-Coulomb che descrivono leggi di comportamento perfettament plastico ed incrudimento lineare. Questi cammini di ritorno costituiscono una base di confronto con algoritmi sviluppati su basi piu' euristiche.
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Rencontré, L.J., Bird, W.W. & Martin, J.B. Internal variable formulation of a backward difference corrector algorithm for piecewise linear yield surfaces. Meccanica 27, 13–24 (1992). https://doi.org/10.1007/BF00452999
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DOI: https://doi.org/10.1007/BF00452999