Metodo della differenza ali'indietro e determinazione dei moduli tangenti per analisi evolutive elastoplastiche a passi finiti

Perego, Umberto

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 1, pp. 75-89.

Riassunto (VO)

Si discute l'applicazione di un procedimento per "differenza all'indietro" ("backward difference") all'integrazione numerica nel tempo di leggi costitutive elastoplastiche e se ne esaminano alcuni aspetti peculiari. Con riferimento a modelli costitutivi isotropi per i quali le funzioni di snervamento dipendono dall'invariante primo delle tensioni, dall'invariante secondo del deviatore delle tensioni e da opportune variabili interne, si ricavano le relazioni non lineari implicite in termini di incrementi finiti, relazioni che esprimono il legame costitutivo del materiale nel passo in base allo schema di integrazione adottato. Coerentemente con tale schema si ricava l'espressione del tensore dei moduli tangenti in una forma unificata che facilita l'implementazione in codici di calcolo automatico.

Abstract

In this paper a backward difference technique is applied to the numerical time integration of elasto-plastic constitutive laws. Reference is made to isotropic constitutive models for which the yield functions depend on the first invariant of the stress tensor, on the second invariant of the stress deviator and on some suitable internal variables. For these models the implicit non-linear relations arising from the adopted integration scheme are established; these relations represent the material constitution in the finite-step. An expression for the "tangent matrix" consistent with such integration scheme is achieved in a unified form which is particularly convenient for computer implementations.

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