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SUMMARY:Two vector Wiener-Hopf equations with 2x2 kernels containing oscil
 latory terms - Pavlos Livasov (Aberystwyth University)
DTSTART:20190816T110000Z
DTEND:20190816T113000Z
UID:TALK128692@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In the first part we discuss a steady-state problem for an int
 erface crack between two dissimilar elastic materials.  We consider a mode
 l of the process zone described by imperfect transmission conditions that 
 reflect the bridging effect along a finite part of the interface in front 
 of the crack. By means of Fourier transform\, the problem is reduced into 
 a Wiener-Hopf equation with a 2x2 matrix\, containing oscillatory terms. W
 e factorize the kernel following an existing numerical method and analyse 
 its performance for various parameters of the problem.  We show that the m
 odel under consideration leads to the classic stress singularity at the cr
 ack tip. Finally\, we derive conditions for the existence of an equilibriu
 m state and compute admissible length of the process zone.  &nbsp\; <br>Fo
 r the second part of the talk\, we consider propagation 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 such a structure\, the fracture of the initially s
 tretched bonds is followed by that of the compressed ones with an unspecif
 ied time-lag. That\, in turn\, reflects the impact of both the internal en
 ergy accumulated inside the pre-stressed interface and the energy brought 
 into the system by external loading. The application to the original probl
 em of continuous (with respect to time) and&nbsp\; selective discrete (wit
 h respect to spatial coordinate) Fourier transforms yields another vector 
 Wiener-Hopf equation with a kernel containing oscillating terms. We use a 
 perturbation technique to factorise the matrix.  &nbsp\;  Finally\, we sho
 w similarities and differences of the matrix-valued kernels mentioned abov
 e and discuss the chosen approaches for their factorisation.
LOCATION:Seminar Room 1\, Newton Institute
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