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[Giulia Curciarello]

Lunedi 1 Dicembre ore 16:00 Aula Magna

Morton E. Gurtin (Carnegie Mellon University, Pittsburgh)

A gradient theory of small-deformation isotropic plasticity that accounts 
for
the Burgers vector and for dissipation due to plastic spin

Abstract :

This study develops a gradient theory of small-deformation viscoplasticity 
that
accounts for the Burgers vector and for dissipation due to plastic spin. 
The theory is based on a system of microforces consistent with its 
peculiar balance; a mechanical version of the second law that includes, 
via the microforces, work performed during viscoplastic flow; a 
constitutive theory that accounts for the Burgers vector through 
dependences on $\scurl\bfH^p$ with $\bfH^p$ the plastic part of the 
elastic-plastic decomposition of the displacement gradient.
 
The microforce balance and the constitutive equations, restricted by the 
second law, are shown to be together equivalent to a flow rule that 
differs from more standard rules in two respects: (i) the underlying 
kinematical rate involves both the plastic strain-rate $\dot{\bfE}^p$ and 
the plastic spin $\dot{\bfW}^p$; (ii) there is an energetic dependence on 
$\scurl\bfH^p$ that yields a backstress. The flow rule may be expressed as 
a pair of coupled second-order partial differential equations, the first 
being an equation for the \emph{plastic strain-rate} in which the stress 
$\bfT$ acts as a driving force, the second, which is independent of 
$\bfT$, as an equation for the \emph{plastic spin}. A consequence of this 
second equation is that \emph{the plastic spin vanishes identically when 
the free energy is independent of} $\scurl\bfH^p$, \emph{but not generally 
otherwise}.

Because of the nonlocal nature of the flow rule, the classical macroscopic 
boundary conditions need be supplemented by nonstandard boundary 
conditions associated with viscoplastic flow.

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