For the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an equivalent stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of "material stability" are assumed. This communication anticipates results to be presented elsewhere in an extended version. Therefore, proofs of the statements and various comments are omitted.
Per l'analisi evolutiva a passi-finiti di sistemi elastoplastici in regime di piccole deformazioni, una proprietà estremale cinematica ed una statica vengono dimostrate in base ai seguenti assunti sulle leggi costitutive: le funzioni di snervamento sono somme di funzioni omogenee del primo ordine nelle tensioni e di limiti di snervamento; questi sono funzioni nonlineari di variabili interne non decrescenti e danno luogo a funzioni energia soggette ad opportune condizioni di convessità. Questa comunicazione presenta risultati da pubblicare in altra sede in forma estesa: qui si omettono le dimostrazioni dei risultati e vari commenti.
@article{RLINA_1988_8_82_4_711_0,
author = {Giulio Maier and Giorgio Novati},
title = {Extremum theorems for finite-step back-ward-difference analysis of elastic-plastic nonlinearly hardening solids},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {82},
year = {1988},
pages = {711-715},
zbl = {0737.73049},
mrnumber = {1139818},
language = {en},
url = {http://dml.mathdoc.fr/item/RLINA_1988_8_82_4_711_0}
}
Maier, Giulio; Novati, Giorgio. Extremum theorems for finite-step back-ward-difference analysis of elastic-plastic nonlinearly hardening solids. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 82 (1988) pp. 711-715. http://gdmltest.u-ga.fr/item/RLINA_1988_8_82_4_711_0/
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