Abstract
In this paper we reconsider the basic concepts of piecewise smooth dissipation functions and yield surfaces in classical plasticity. This re-examination is from the perspective of convex analysis, and is applied to an internal variable description of the elastic-plastic solid. First, we recapitulate the arguments in which the yield surface is a derived concept in a theory which assumes the existence of a positive semi-definite quadratic strain energy function and a convex homogeneous dissipation function, in the case where the dissipation function is differentiable everywhere except at the origin. We then consider the case of a multiplicity of dissipation mechanisms, and the determination of the operative mechanism or mechanisms. The global dissipation function is theconvex hull of the local dissipation functions. A piecewise smooth yield function follows through a generalization of the transformation for the smooth case.
Sommario
La presente Memoria riprende in esame, nell'ottica dell'analisi convessa, i concetti di funzioni di dissipazione e di superfici di snervamento generalmente regolari, fondamentali nella plasticità classica, applicandoli nel contesto di una descrizione del solido elasto-plastico mediante variabili interne. Innanzitutto si ricordano le argomentazioni per cui la superficie di snervamento è un concetto derivato in una teoria che assume l'esistenza di una funzione ‘energia di deformazione’ quadratica e positiva semidefinita e di una funzione ‘dissipazione’ convessa e omogenea, nel caso in cui la funzione dissipazione è differenziabile ovunque tranne che nell'origine. Si considera quindi il caso di una molteplicità di meccanismi operativi. La funzione dissipazione globale è l'inviluppo convesso delle funzioni dissipazione locali; ne consegue, attraverso una generalizzazione della trasformazione nel caso di regolarità, una funzione di snervamento generalmente regolare.
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General Lecture delivered at the 11th Italian National Congress of Theoretical and Applied Mechanics (AIMETA), Trento, September 1992.
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Martin, J.B., Reddy, B.D. Piecewise smooth dissipation and yield functions in plasticity. Meccanica 28, 169–175 (1993). https://doi.org/10.1007/BF00989118
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DOI: https://doi.org/10.1007/BF00989118