Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to compute the atomic stress objectively?   Atomistic simulation has been a powerful study tool in mechanics research,
but how to objectively compute the atomic stress equivalent to Cauchy stress is
still controversial, especially on the velocity-related part in the virial
stress definition. In this paper, by strictly following the classical
definition of the Cauchy stress for continuum medium, the fundamental
Lagrangian atomic stress is proposed and can be used to obtain the correct
Cauchy stress under any circumstances. Furthermore, the Lagrangian virial
stress is proposed, which is still in virial form but does not include
velocities to avoid controversial velocity treatments. It is also found that
the widely used classical virial stress is actually the Eulerian virial stress,
which includes the velocities of atoms, and is valid only when the
impulse-momentum theorem is applicable to estimate the internal forces. However
this requirement for the Eulerian atomic stress can not always be met in
practical cases, such as the material volume element in rotation and the
examples presented in this paper, but the proposed Lagrangian atomic stress can
avoid these velocity-related nonobjectivities.

23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg