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SUMMARY:Understanding dynamic crack growth in structured systems with the 
 Wiener-Hopf technique: Lecture 1 - Michael Nieves (Keele University\; Univ
 ersity of Cagliari\; University of Liverpool)
DTSTART:20190806T131500Z
DTEND:20190806T143000Z
UID:TALK128104@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> 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 &nbsp\;
 in discrete periodic &nbsp\;media. We begin with the model of a lattice sy
 stem containing &nbsp\;a crack and show how this can be reduced to a scala
 r Wiener-Hopf &nbsp\;equation &nbsp\;through &nbsp\;the Fourier &nbsp\;tra
 nsform. &nbsp\;From &nbsp\;this functional &nbsp\;equation &nbsp\;we ident
 ify &nbsp\;all possible &nbsp\;dynamic &nbsp\;processes &nbsp\;complementi
 ng&nbsp\; &nbsp\;the &nbsp\;crack &nbsp\;growth. &nbsp\;We &nbsp\;determin
 e &nbsp\;the &nbsp\;solution &nbsp\;to &nbsp\;the problem &nbsp\;and &nbsp
 \;how &nbsp\;this &nbsp\;is &nbsp\;used &nbsp\;to &nbsp\;predict &nbsp\;cr
 ack &nbsp\;growth &nbsp\;regimes &nbsp\;in &nbsp\;numerical &nbsp\;simulat
 ions. &nbsp\;Other applications of the adopted method\, including the anal
 ysis of the progressive collapse of large-scale structures\, are discussed
 .<br><span><br>  <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 instabilities\, J. Mech. Phys. Solids 43\, no. 1\, 
 1-  48.  &nbsp\;  [2] Slepyan\, L.I. (2001): Feeding and dissipative &nbsp
 \;waves in fracture and phase transition &nbsp\;I. Some 1D  structures and
  a square-cell lattice\, J. Mech. Phys. Solids 49\, 469-511.  &nbsp\;  [3]
  Slepyan\, L.I. (2002): Models and Phenomena&nbsp\; in Fracture Mechanics\
 , Foundations &nbsp\;of Engineering  Mechanics\, Springer.  &nbsp\;  [4] M
 ishuris\, G.S.\, Movchan\, A.B. and Slepyan\, L.I.\, (2007): Waves and fra
 cture in an inhomogeneous lattice structure\, Wave Random Complex 17\, no.
  4\, 409-428.  &nbsp\;  [5] Brun\, M.\, Giaccu\, G.F.\, Movchan\, A.B.\, a
 nd Slepyan\, L. I.\, (2014): Transition wave in the collapse of the San Sa
 ba Bridge\, Front. Mater. 1:12. doi: 10.3389/fmats.2014.00012.  &nbsp\;  [
 6] Nieves\, M.J.\, Mishuris\, &nbsp\;G.S.\, Slepyan\, &nbsp\;L.I.\, (2016)
 : Analysis &nbsp\;of dynamic &nbsp\;damage propagation &nbsp\;in discrete 
 beam structures\, Int. J. Solids Struct. 97-98\, 699-713.    </span><br><b
 r><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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