Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of the stress concentration in high-contrast elastic
  composites   A long-standing area of materials science research has been the study of
electrostatic, magnetic, and elastic fields in composite with densely packed
inclusions whose material properties differ from that of the background. For a
general elliptic system, when the coefficients are piecewise H\"{o}lder
continuous and uniformly bounded, an $\varepsilon$-independent bound of the
gradient was obtained by Li and Nirenberg \cite{ln}, where $\varepsilon$
represents the distance between the interfacial surfaces. However, in
high-contrast composites, when $\varepsilon$ tends to zero, the stress always
concentrates in the narrow regions. As a contrast to the uniform boundedness
result of Li and Nirenberg, in order to investigate the role of $\varepsilon$
played in such kind of concentration phenomenon, in this paper we establish the
blow-up asymptotic expressions of the gradients of solutions to the Lam\'{e}
system with partially infinite coefficients in dimensions two and three. We
discover the relationship between the blow-up rate of the stress and the
relative convexity of adjacent surfaces, and find a family of blow-up factor
matrices with respect to the boundary data. Therefore, this work completely
solves the Babu\u{s}ka problem on blow-up analysis of stress concentration in
high-contrast composite media. Moreover, as a byproduct of these local
analysis, we establish an extended Flaherty-Keller formula on the global
effective elastic property of a periodic composite with densely packed fibers,
which is related to the "Vigdergauz microstructure" in the shape optimization
of fibers.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess