Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A blend of stretching and bending in nematic polymer networks   Nematic polymeric networks are (heat and light) activable materials, which
combine the features of rubber and nematic liquid crystals. When only the
stretching energy of a thin sheet of nematic polymeric network is minimized,
the intrinsic (Guassian) curvature of the shape it takes upon (thermal or
optical) actuation is determined. This, unfortunately, produces a multitude of
possible shapes, for which we need a selection criterion, which may only be
provided by a correcting bending energy depending on the extrinsic curvatures
of the deformed shape. The literature has so far offered approximate
corrections depending on the mean curvature. In this paper, we derive the
appropriate bending energy of a sheet of polymeric nematic network from the
celebrated neo-classical energy of nematic elastomers in three space
dimensions. This task is performed via a dimension reduction based on a
modified Kirchhoff-Love hypothesis, which withstands to the criticism of more
sophisticated analytical tools. The result is a surface elastic free-energy
density where stretching and bending are blended together; they may or may not
be length-separated, and should be minimized together. The extrinsic curvatures
of the deformed shape not only feature in the bending energy through the mean
curvature, but also through the relative orientation of the nematic director in
the frame of the directions of principal curvature.

31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
9
The categories of this paper are: nlin