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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