Computational modeling issues of gradient-extended viscoplasticity

Paper in proceeding, 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.