Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A unification of finite deformation $J_2$ Von-Mises plasticity and
  quantitative dislocation mechanics   We present a framework which unifies classical phenomenological $J_2$ and
crystal plasticity theories with quantitative dislocation mechanics. The theory
allows the computation of stress fields of arbitrary dislocation distributions
and, coupled with minimally modified classical ($J_2$ and crystal plasticity)
models for the plastic strain rate of statistical dislocations, results in a
versatile model of finite deformation mesoscale plasticity. We demonstrate some
capabilities of the framework by solving two outstanding challenge problems in
mesoscale plasticity: 1) recover the experimentally observed power-law scaling
of stress-strain behavior in constrained simple shear of thin metallic films
inferred from micropillar experiments which all strain gradient plasticity
models overestimate and fail to predict; 2) predict the finite deformation
stress and energy density fields of a sequence of dislocation distributions
representing a progressively dense dislocation wall in a finite body, as might
arise in the process of polygonization when viewed macroscopically, with one
consequence being the demonstration of the inapplicability of current
mathematical results based on $\mathrm{\Gamma}$-convergence for this physically
relevant situation. Our calculations in this case expose a possible `phase
transition' - like behavior for further theoretical study. We also provide a
quantitative solution to the fundamental question of the volume change induced
by dislocations in a finite deformation theory, as well as show the massive
non-uniqueness in the solution for the (inverse) deformation map of a body
inherent in a model of finite strain dislocation mechanics, when approached as
a problem in classical finite elasticity.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys