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.


Kristoffer Carlsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Magnus Ekh

Chalmers, Applied Mechanics, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Kenneth Runesson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Svenska Mekanikdagar, 10-12 juni, Linköping, 2015 (1 page abstract)

Subject Categories

Metallurgy and Metallic Materials

Areas of Advance

Materials Science

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