dislocation mechanics

In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use Cartan's moving frames to describe the distorted lattice structure via differential 1-forms. In this theory the primary fields are the dislocation fields, defined as a collection of differential 2-forms. The defect content of the lattice structure is then determined by the superposition of the dislocation fields.

We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented. The model is a minimal enhancement of classical crystal/J_2 plasticity that fundamentally accounts for polar/excess dislocations at the mesoscale. It has the ability to compute the static and dynamic finite deformation stress fields of arbitrary (evolving) dislocation distributions in finite bodies of arbitrary shape and elastic anisotropy under general boundary conditions. This capability is used to present a comparison of the static stress fields, at finite and small deformations, for screw and edge dislocations, revealing heretofore unexpected differences. The computational framework is verified against the sharply contrasting predictions of geometrically linear and nonlinear theories for the stress field of a spatially homogeneous dislocation distribution in the body, as well as against other exact results of the theory. Verification tests of the time-dependent numerics are also presented. Size effects in crystal and isotropic versions of the theory are shown to be a natural consequence of the model and are validated against available experimental data. With inertial effects incorporated, the development of an (asymmetric) propagating Mach cone is demonstrated in the finite deformation theory when a dislocation moves at speeds greater than the linear elastic shear wave speed of the material.

Paper can be found at link Finite_Deformation_Dislocation_Mechanics.

Y. S. Chen, W. Choi, S. Papanikolaou, M. Bierbaum, J. P. Sethna

Topic: Towards zero prototyping in ceramic component design

European Commission' s JRC (Joint Research Centre) is organizing the 3rd workshop on physics based material models and experimental observations (http://iwpmeo.org/) in collaboration with University of Oxford, Max-Planck-Institut für Eisenforschung and Middle East Technical University. The workshop will be held in Izmir/Turkey on 2-4 June 2014.

Yichao Zhu       Stephen J. Chapman       Amit Acharya

(to appear in Journal of the Mechanics and Physics of Solids)

In the theory of dislocations, the Burgers vector is usually defined by referring to a crystal structure. Using the notion of affine development of curves on a differential manifold with a connection, we give a differential geometric definition of the Burgers vector directly in the continuum setting, without making use of an underlying crystal structure.

(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

‚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).

Luc Tartar and Amit Acharya

Bulletin of the Italian Mathematical Union, (9)IV, 409-444, 2011

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.