(This paper is to appear in the IUTAM Procedia on "Linking scales  in
computations: from microstructure to macro-scale properties," edited by
Oana Cazacu)

Amit Acharya, S. Jonathan Chapman

With a view towards utilization in macroscopic continuum models, an approximation to the root-mean-square of the driving force field on individual dislocations within a "representative volume element" is derived. The plastic flow field of individual dislocations is also similarly averaged. Even under strong simplifying assumptions, non-trivial results on the origin and nature of anisotropic macroscopic yielding, plastic spin, and the plastic flow rule (for single and polycrystalline bodies) are obtained. A particular result is the dependence of the plastic response of a material point of the averaged model on the presence of dislocations within it, an effect absent in conventional theories of plastic response (e.g., J2 plasticity). Also noteworthy is the explicit geometric accounting of the indeterminacy of the slip-plane identity of the screw dislocation that appears to lead to some differences with conventional ideas.

‚Source truncation and exhaustion: Insights from quantitative in-situ
TEM tensile testing' by D. Kiener and A.M. Minor (http://dx.doi.org/10.1021/nl201890s).

The scientific community was challenged by explaining the uncommon
mechanical properties of microscopic samples, leading to the emergence
of two major schools of thought. One group argued that in miniaturized
samples accordingly small dislocations (the carrier of plastic
deformation) will lead to the extraordinarily strength, while the other
envisioned that only pristine volumes could exhibit such high strength.

(Paper to appear in Bollettino della Unione Matematica Italiana - Bulletin of the Italian Mathematical Union)

Luc Tartar and Amit Acharya

Global existence and uniqueness results for a quasilinear system of partial differential equations in one space dimension and time representing the transport of dislocation density are obtained. Stationary solutions of the system are also studied, and an infinite dimensional class of equilibria is derived. These time (in)dependent solutions include both periodic and aperiodic spatial distributions of smooth fronts of plastic distortion representing dislocation twist boundary microstructure. Dominated by hyperbolic transport-like features and at the same time containing a large class of equilibria, our system differs qualitatively from regularized systems of hyperbolic conservation laws and neither does it fit into a gradient flow structure.

A field theory of dislocation mechanics and plasticity is illustrated through new results at the nano, meso, and macro scales. Specifically, dislocation nucleation, the occurrence of wave-type response in quasi-static plasticity, and a jump condition at material interfaces and its implications for analysis of deformation localization are discussed.