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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Two vector Wiener-Hopf equations with 2x2 kernels
containing oscillatory terms - Pavlos Livasov (Abe
rystwyth University)
DTSTART;TZID=Europe/London:20190816T120000
DTEND;TZID=Europe/London:20190816T123000
UID:TALK128692AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128692
DESCRIPTION:In the first part we discuss a steady-state proble
m for an interface crack between two dissimilar el
astic materials. We consider a model of the proce
ss zone described by imperfect transmission condit
ions that reflect the bridging effect along a fini
te part of the interface in front of the crack. By
means of Fourier transform\, the problem is reduc
ed into a Wiener-Hopf equation with a 2x2 matrix\,
containing oscillatory terms. We factorize the ke
rnel following an existing numerical method and an
alyse its performance for various parameters of th
e problem. We show that the model under considera
tion leads to the classic stress singularity at th
e crack tip. Finally\, we derive conditions for th
e existence of an equilibrium state and compute ad
missible length of the process zone. \;

For the second part of the talk\, we consider prop
agation of a dynamic crack in a periodic structure
with internal energy. The structural interface is
formed by a discrete set of uniformly distributed
alternating compressed and stretched bonds. In su
ch a structure\, the fracture of the initially str
etched bonds is followed by that of the compressed
ones with an unspecified time-lag. That\, in turn
\, reflects the impact of both the internal energy
accumulated inside the pre-stressed interface and
the energy brought into the system by external lo
ading. The application to the original problem of
continuous (with respect to time) and \; selec
tive discrete (with respect to spatial coordinate)
Fourier transforms yields another vector Wiener-H
opf equation with a kernel containing oscillating
terms. We use a perturbation technique to factoris
e the matrix. \; Finally\, we show similari
ties and differences of the matrix-valued kernels
mentioned above and discuss the chosen approaches
for their factorisation.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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