Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Riemannian approach to the membrane limit in non-Euclidean elasticity   Non-Euclidean, or incompatible elasticity is an elastic theory for
pre-stressed materials, which is based on a modeling of the elastic body as a
Riemannian manifold. In this paper we derive a dimensionally-reduced model of
the so-called membrane limit of a thin incompatible body. By generalizing
classical dimension reduction techniques to the Riemannian setting, we are able
to prove a general theorem that applies to an elastic body of arbitrary
dimension, arbitrary slender dimension, and arbitrary metric. The limiting
model implies the minimization of an integral functional defined over
immersions of a limiting submanifold in Euclidean space. The limiting energy
only depends on the first derivative of the immersion, and for
frame-indifferent models, only on the resulting pullback metric induced on the
submanifold, i.e., there are no bending contributions.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org