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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Cluster method in the theory of fibrous elastic co
mposites - Vladimir Mityushev (Akademia Pedagogic
zna)
DTSTART;TZID=Europe/London:20191101T100000
DTEND;TZID=Europe/London:20191101T110000
UID:TALK133588AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133588
DESCRIPTION:Consider a 2D multi-phase random composite with di
fferent circular inclusions. A finite number $n$ o
f inclusions on the infinite plane forms a cluster
. The corresponding boundary value problem for Mus
khelishvili'\;s potentials is reduced to a syst
em of functional equations. Solution to the funct
ional equations can be obtained by a method of suc
essive approximations or by the Taylor expansion o
f the unknown analytic functions. Next\, the loca
l stress-strain fields are calculated and the aver
aged elastic constants are obtained in symbolic fo
rm. Extensions of Maxwell'\;s approach and othe
r various self-consisting methods are discussed. A
n uncertainty when the number of elements $n$ in a
cluster tends to infinity is analyzed by means of
the conditionally convergent series. Basing on th
e fields around a finite cluster without clusters
interactions one can deduce formulae for the effec
tive constants only for dilute clusters. The Eisen
stein summation yields new analytical formulae for
the effective constants for random 2D composites
with high concentration of inclusions.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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