Abstract
We provide optimal a priori estimates for finite element approximations of a model of rate-independent single-crystal strain-gradient plasticity. The weak formulation of the problem takes the form of a variational inequality in which the primary unknowns are the displacement and slips on the prescribed slip systems, as well as the back-stress associated with the vectorial microstress. It is shown that the return mapping algorithm for local plasticity can be applied element-wise to this non-local setting. Some numerical examples illustrate characteristic features of the non-local model.
| Original language | English |
|---|---|
| Pages (from-to) | 784-804 |
| Number of pages | 21 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 90 |
| Issue number | 6 |
| DOIs | |
| State | Published - 11 May 2012 |
Keywords
- A priori finite element estimates
- Closest-point projection
- Rate-independent
- Single crystal
- Strain-gradient plasticity
- Variational inequality