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SUMMARY:Understanding dynamic crack growth in structured systems with the 
 Wiener-Hopf technique: Lecture 2 - Michael Nieves (Keele University\; Univ
 ersity of Cagliari\; University of Liverpool)
DTSTART:20190809T131500Z
DTEND:20190809T143000Z
UID:TALK128317@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Crack propagation is a process accompanied by multiple p
 henomena at different scales. In particular\, when a crack grows\, microst
 ructural &nbsp\;vibrations are released\, emanating from the crack tip. Co
 ntinuous&nbsp\; &nbsp\;models&nbsp\; &nbsp\;of &nbsp\;dynamic&nbsp\; &nbsp
 \;cracks&nbsp\; &nbsp\;are &nbsp\;well &nbsp\;known&nbsp\; &nbsp\;to &nbsp
 \;omit &nbsp\;information&nbsp\; &nbsp\;concerning&nbsp\; &nbsp\;these mic
 rostructural processes [1]. On the other hand\, tracing these vibrations o
 n the microscale is possible if one considers a crack propagating in a str
 uctured system\, such as a lattice [2\, 3]. &nbsp\;These models have a par
 ticular relevance in the design of metamaterials\, &nbsp\;whose microstruc
 ture &nbsp\;can be tailored to control dynamic effects for a variety of pr
 actical purposes [4]. Similar approaches have been recently paving new pat
 hways to understanding failure processes in civil engineering systems [5\,
  6].  &nbsp\; <br></span><br><span>In this lecture\, we aim to demonstrate
  the importance of the Wiener-Hopf technique in the analysis and solution 
 &nbsp\;of problems &nbsp\;concerning &nbsp\;waves and crack propagation &n
 bsp\;in discrete periodic &nbsp\;media. We begin with the model of a latti
 ce system containing &nbsp\;a crack and show how this can be reduced to a 
 scalar Wiener-Hopf &nbsp\;equation &nbsp\;through &nbsp\;the Fourier &nbsp
 \;transform. &nbsp\;From &nbsp\;this functional &nbsp\;equation &nbsp\;we 
 identify &nbsp\;all possible &nbsp\;dynamic &nbsp\;processes &nbsp\;comple
 menting&nbsp\; &nbsp\;the &nbsp\;crack &nbsp\;growth. &nbsp\;We &nbsp\;det
 ermine &nbsp\;the &nbsp\;solution &nbsp\;to &nbsp\;the problem &nbsp\;and 
 &nbsp\;how &nbsp\;this &nbsp\;is &nbsp\;used &nbsp\;to &nbsp\;predict &nbs
 p\;crack &nbsp\;growth &nbsp\;regimes &nbsp\;in &nbsp\;numerical &nbsp\;si
 mulations. &nbsp\;Other applications of the adopted method\, including the
  analysis of the progressive collapse of large-scale structures\, are disc
 ussed.  &nbsp\;  <b><i><br></i></b></span><b><i><br></i></b><span><span><b
 ><i>R</i></b><b><i>efere</i></b><b><i>n</i></b><b><i>ce</i></b><b><i>s</i>
 </b></span>  [1] Marder\, M. and Gross\, S. (1995): Origin of crack tip in
 stabilities\, J. Mech. Phys. Solids 43\, no. 1\, 1-  48.  &nbsp\;  [2] Sle
 pyan\, L.I. (2001): Feeding and dissipative &nbsp\;waves in fracture and p
 hase transition &nbsp\;I. Some 1D  structures and a square-cell lattice\, 
 J. Mech. Phys. Solids 49\, 469-511.  &nbsp\;  [3] Slepyan\, L.I. (2002): M
 odels and Phenomena&nbsp\; in Fracture Mechanics\, Foundations &nbsp\;of E
 ngineering  Mechanics\, Springer.  &nbsp\;  [4] Mishuris\, G.S.\, Movchan\
 , A.B. and Slepyan\, L.I.\, (2007): Waves and fracture in an inhomogeneous
  lattice structure\, Wave Random Complex 17\, no. 4\, 409-428.  &nbsp\;  [
 5] Brun\, M.\, Giaccu\, G.F.\, Movchan\, A.B.\, and Slepyan\, L. I.\, (201
 4): Transition wave in the collapse of the San Saba Bridge\, Front. Mater.
  1:12. doi: 10.3389/fmats.2014.00012.  &nbsp\;  [6] Nieves\, M.J.\, Mishur
 is\, &nbsp\;G.S.\, Slepyan\, &nbsp\;L.I.\, (2016): Analysis &nbsp\;of dyna
 mic &nbsp\;damage propagation &nbsp\;in discrete beam structures\, Int. J.
  Solids Struct. 97-98\, 699-713.  </span><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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