Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density-based crystal plasticity : from the discrete to the continuum   Because of the enormous range of time and space scales involved in
dislocation dynamics, plastic modeling at macroscale requires a continuous
formulation. In this paper, we present a rigorous formulation of the transition
between the discrete, where plastic flow is resolved at the scale of individual
dislocations, and the continuum, where dislocations are represented by
densities. First, we focus on the underlying coarse-graining procedure and show
that the emerging correlation-induced stresses are scale-dependent. Each of
these stresses can be expanded into the sum of two components. The first one
depends on the local values of the dislocation densities and always opposes the
sum of the applied stress and long-range mean field stress generated by the
geometrically necessary dislocation (GND) density; this stress acts as a
friction stress. The second component depends on the local gradients of the
dislocation densities and is inherently associated to a translation of the
elastic domain; therefore, it acts as a back-stress. We also show that these
friction and back- stresses contain symmetry-breaking components that make the
local stress experienced by dislocations to depend on the sign of their Burgers
vector.

14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
19
The categories of this paper are: eess
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci