Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward the mechanics of fractal materials: mechanics of continuum with
  fractal metric   This paper is devoted to the mechanics of fractal materials. A continuum
framework accounting for the topological and metric properties of fractal
domains in heterogeneous media is developed. The kinematics of deformations is
elucidated and the symmetry of the Cauchy stress tensor is established. The
mapping of mechanical problems for fractal materials into the corresponding
problems for the fractal continuum is discussed. Stress and strain
distributions in elastic fractal bars are analyzed. Some features of acoustic
wave propagation and localization in scale-invariant media are briefly
discussed. The effect of fractal correlations in the material microstructure on
the crack mechanics is revealed. It is shown that the fractal nature of
heterogeneity can either delay or assist the crack initiation and propagation,
depending on the interplay between metric and topological properties of the
fractal domain.

2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg