Sommario
Si svolgono alcune considerazioni sui fenomeni di biforcazione in solidi elastoplastici in regime di “piccole deformazioni” (di linearità geometrica) e precisamente sul manifestarsi di localizzazioni intese come discontinuità nel campo delle deformazioni incrementali. Si considerano leggi nonassociate. Vengono così inclusi nella trattazione modelli costitutivi frequentemente adottati per descrivere il comportamento di materiali ad attrito interno e soggetti a danneggiamento (nel senso di degrado di rigidezze elastiche in seguito a deformazioni anelastiche), oltre che soggetti a manifestazioni di instabilità per incrudimento negativo (“softening”). Si esamina criticamente il criterio, frequentemente adottato in letteratura, di localizzazione fondato su “materiale di confronto” incrementalmente lineare e si fornisce, corredato da osservazioni comparative, il criterio che risulta dall'assunzione del modello di materiale incrementale non lineare
Summary
This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear “comparison material” is critically reviewed and compared to the criterion resulting from “actual” nonlinear plastic flow laws.
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Borré, G., Maier, G. On linear versus nonlinear flow rules in strain localization analysis. Meccanica 24, 36–41 (1989). https://doi.org/10.1007/BF01576001
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DOI: https://doi.org/10.1007/BF01576001