Meccanica

, Volume 2, Issue 1, pp 55–64 | Cite as

On elastic-plastic structures with associated stress-strain relations allowing for work softening

  • Giulio Maier
Article

Summary

For the elementary (finite or infinitesimal) constituents of the structure are assumed generalized stress-strain relations which satisfy the condition of “normality” but which may exhibit “work-softening”, concavity of yield surfaces, variation of elastic coefficients with stress and/or plastic strain.

The usual phenomena of geometric instability are excluded. Sufficient conditions are formulated for overall stability in spite of the presence of unstable elements, and for uniqueness of the incremental boundary-values problem. Conditions are discussed with a view to applications and expressed in terms of positive definiteness of appropriate quadratic forms.

Finally, yield surfaces and flow laws for the structure are examined, and among other things their necessary “association” is shown.

Keywords

Mechanical Engineer Civil Engineer Plastic Strain Alla Quadratic Form 

Sommario

Per i costituenti elementari (finiti o infinitesimi) della struttura si assumono legami incrementali tra sforzi e deformazioni generalizzati che soddisfano alla condizione di “normalità” ma che per il resto sono generici, cioè tali da presentare eventualmente “incrudimento negativo”, concavità del campo elastico, variazione dei coefficienti elastici con gli sforzi e/o con le deformazioni plastiche.

Esclusi per il sistema i fenomeni usuali di instabilità geometrica si formulano condizioni sufficienti per la stabilità del complesso nonostante la presenza di parti a funzionamento instabile, e per l'unicità del problema incrementale al contorno. Le condizioni sono discusse in vista delle applicazioni ed espresse in termini di definizione positiva di forme quadratiche opportune.

Si esaminano infine le superfici di snervamento e le leggi di scorrimento per l'intera struttura e, tra l'altro, se ne dimostra la necessaria “associazione”.

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Copyright information

© Tamburini Editore 1966

Authors and Affiliations

  • Giulio Maier
    • 1
  1. 1.Istituto di Scienza delle costruzioniPolitecnico di MilanoItaly

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