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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Potential new pathways in modelling sea ice phenom
ena coming from the analysis of multiscale solids
with defects - Michael Nieves (Keele University\;
University of Cagliari\; University of Liverpool)
DTSTART;TZID=Europe/London:20171206T153000
DTEND;TZID=Europe/London:20171206T163000
UID:TALK96604AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/96604
DESCRIPTION:In this talk\, we discuss two methods used in the
modelling of materials with defects at different s
cales. \; The first\, known as the method o
f mesoscale asymptotic approximations [1]\, \
;is appropriate for the modelling of granular mate
rials. In particular\, we discuss the approximatio
n of solutions to a particular class of transmissi
on problems in solids containing clusters of many
small inclusions\, which can interact with each ot
her [2]. The asymptotics are supplied with remaind
er estimates that are rigorously justified. \;
\; The second method concerns the dynamic
failure of structured materials\, commonly used in
understanding the phenomena involved at multiple
scales in the fracture of solids. The subject has
been explored in the last 30 years for a variety o
f mass-spring systems [3]. \; Here\, we take
a different approach and consider faults propagati
ng through periodic mass-beam systems [4\, 5]\, wh
ich are more commonly found in civil engineering a
pplications such as long rooftops\, bridges and pi
peline systems. We give a summary of analytical re
sults\, based on the Fourier transform and the Wie
ner-Hopf technique\, concerning the dynamic behavi
our of the structure during the failure. \;
Numerical simulations demonstrate the effectivene
ss of both approaches. It is envisaged that both
techniques may find a new home in the modelling of
phenomena associated with the behaviour of sea ic
e. \; **References:** \; [1] V. Maz&rsquo\;ya\, A. Movchan and M. Nieves
\, (2013): Green&rsquo\;s Kernels and Meso-Scale A
pproximations in Perforated Domains\, Lecture Note
s in Mathematics 2077\, Springer. [2] M.J. Nieves
\, (2017): Asymptotic analysis of solutions to tra
nsmission problems in solids with many inclusions\
, SIAM J. Appl. Math. 77 (4)\, 1417-1443. [3] L.I
. Slepyan\, \;(2002): Models and Phenomena in
Fracture Mechanics\, Foundations of Engineering M
echanics\, Springer. [4] M.J. Nieves\, G.S. Mishu
ris\, L.I. Slepyan\, (2016): Analysis of dynamic d
amage propagation in discrete beam structures\, In
t. J. Solids Struct. 97-98\, 699-713. \; [5]
M.J. Nieves\, G.S. Mishuris\, L.I. Slepyan\, (2017
): Transient wave in a transformable periodic flex
ural structure\, Int. J. Solids Struct. 112\, 185-
208

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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