Computational modeling issues of gradient-extended viscoplasticity
Paper in proceedings, 2015
Crystal (visco)plasticity is the accepted model framework for incorporating microstructural in-
formation in continuum theory with application to crystalline metals where dislocations constitute the
physical mechanism behind inelastic deformation. In order to account for the size effects due to the ex-
istence of grain boundaries in a polycrystal, it is convenient to include some sort of gradient-extension
of the flow properties along the slip directions, either in the dragstress or backstress (from GND, which
are generally of two types: edge and screw dislocations). Various explicit models based on this con-
ceptual background have been proposed, not the least by Gurtin and coworkers 1 ; however, several
modeling issues still await its resolution. An elegant way of unifying gradient theory for different
application models was presented by Miehe 2 .
In this contribution we focus on issues related to the theoretical as well as the computational
format, while (for the sake of clarity) restricting to gradient-extended viscoplasticity for a standard
continuum. Thereby, we avoid the additional complications associated with the proper version of
crystal (visco) plasticity, such as higher order boundary conditions. The so-called “primal” format
exploits the internal variables as the primary unknown field together with the displacement field. An
alternative format is coined the “semi-dual format”, which exploits (in addition) the microstresses,
thereby defining a mixed variational problem. We note that a mixed method that bears resemblance
with the semi-dual format has been used extensively in our research group in recent years 3 ; however,
without possessing a well-defined variational structure.
We compare the primal and semi dual variational formats in terms of pros and cons from various
aspects. We also discuss the pertinent FE-spaces that appear as the natural/possible choices. In partic-
ular, for the semi-dual format we investigate the possibility to use a minimal degree of regularity that
has so far not been discussed in the literature.