### Tuesday, 12 October 2004 - 1:00 PM

### This presentation is part of : Rajagopal Symposium

### Finite-deformation Plasticity With and Without Elastic Isotropy

**Sia Nemat-Nasser**, UC San Diego, UC San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0416
Building on our current experimentally-supported understanding of dislocation-based slip-induced metal plasticity, I will re-examine some of the fundamentals of continuum elastoplasticity. I will show that the usual multiplicative decomposition of the deformation gradient into a plastic and an accompanying elastic deformation gradient implies a number of direct relations among various rate quantities in such a manner that, given the velocity gradient and the plastic deformation rate tensor, all other rate kinematical variables can be calculated exactly. If the material is elastically isotropic, then all rate kinematical and dynamical quantities can be computed when an elastic potential is also given in terms of the basic invariants of, say, the elastic stretch tensor (or its equivalent). The case of elastic anisotropy is then examined and it is shown that, in general, it is not appropriate to seek to define the “plastic spin” by a constitutive relation. For a polycrystalline solid consisting of a very large number of crystals, and hence slip systems, a new formulation is presented for the plastic velocity gradient that helps to clarify the question of plastic spin.

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