Energetic Approach to Large Strain Gradient Crystal Plasticity

Strain gradient plasticity under non-proportional loading

A critical examination is made of two classes of strain gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quantities expressed in terms of increments of strains and their gradients, whereas the other class employs incremental relationships between all stress quantities and the increments of strains and their g...

Guidelines for Constructing Strain Gradient Plasticity Theories

Issues related to the construction of continuum theories of strain gradient plasticity which have emerged in recent years are reviewed and brought to bear on the formulation of the most basic theories. Elastic loading gaps which can arise at initial yield or under imposition of non-proportional incremental boundary conditions are documented and analytical methods for dealing with them are illus...

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...

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...