Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deterministic calculation of elasto-plastic stress-strain behavior from
  arbitrary deformation fields   A system of partial differential equations is derived to compute the
full-field stress from an observed strain field when the plastic component of
the material constitutive equation is unknown. These equations generalize
previously proposed equations that are valid in the case where the elastic
strain is negligible. The system of equations assume that the constitutive
relations are isotropic, but otherwise make few assumptions and can be directly
applied (without modification) to cases of finite deformation, non-linear
elasticity and plasticity, compressible materials, rate dependent materials,
and a variety of different yield surface shapes and hardening laws. Unlike the
prior linear hyperbolic partial differential equations, this system of
equations is non-linear and time dependent. The newly proposed equations can be
used to solve for the stress field (and hence constitutive equation), for
arbitrary geometries and loading conditions when the full-field strain is
known. This generalization resolves a significant challenge in computing the
stress during elasto-plastic deformations: some regions of the material will be
elastically unloading while others are undergoing significant plastic
deformation. This problem significantly limited applications of the previously
proposed equations, but is fully resolved here.
  A two-dimensional case study of necking in a uniaxial tensile test specimen
is investigated to illustrate the method. The governing equations are
numerically solved using an algorithm based on on the finite volume method
developed in an accompanying work. This is validated against the solution to
the forward problem and shown to give accurate results (within numerical error
of the true solution). This case study thus demonstrates that the developed
approach has unique capabilities, including the first theoretically exact
solution to this well studied problem.

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The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph