Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theories for incompressible rods: a rigorous derivation via
  $\Gamma$-convergence   We use variational convergence to derive a hierarchy of one-dimensional rod
theories, starting out from three-dimensional models in nonlinear elasticity
subject to local volume-preservation. The densities of the resulting
$\Gamma$-limits are determined by minimization problems with a trace constraint
that arises from the linearization of the determinant condition of
incompressibility. While the proofs of the lower bounds rely on suitable
constraint regularization, the upper bounds require a careful, explicit
construction of locally volume-preserving recovery sequences. After decoupling
the cross-section variables with the help of divergence-free extensions, we
apply an inner perturbation argument to enforce the desired non-convex
determinant constraint. To illustrate our findings, we discuss the special case
of isotropic materials.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg