Equivalent plastic strain gradient enhancement of single crystal plasticity: theory and numerics

Some links between Cosserat, strain gradient crystal plasticity and the statistical theory of dislocations

Finite Element Analysis and Algorithms for Single-Crystal Strain-Gradient Plasticity

We provide optimal a priori estimates for nite 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...

Dynamic Stability of Single Walled Carbon Nanotube Based on Nonlocal Strain Gradient Theory

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano-...

Relaxation of the single-slip condition in strain-gradient plasticity.

We consider the variational formulation of both geometrically linear and geometrically nonlinear elasto-plasticity subject to a class of hard single-slip conditions. Such side conditions typically render the associated boundary-value problems non-convex. We show that, for a large class of non-smooth plastic distortions, a given single-slip condition (specification of Burgers vectors) can be rel...

Pile - up studies in dislocation - based single crystal gradient plasticity

/department of mechanical engineering Introduction In plastic deformations, which arise due to the motion of dislocations in crystalline microstructure, size effects cannot be neglected at a small scales of observation. Within each grain of a polycrystal, the grain boundaries act as natural obstacles to dislocation motion. Due to the stresses dislocations exert onto each other, dislocations wil...