BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Dynamic stability of structures under high loading rates by locali
 zed perturbation approach - Professor Nicolas Triantafyllidis\, Ecole Poly
 technique
DTSTART:20160226T140000Z
DTEND:20160226T150000Z
UID:TALK63282@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:Of interest here is the stability of structures subjected to h
 igh loading rates where inertia is taken into account. The approach curren
 tly used in the literature to analyze these stability problems is the meth
 od of modal analysis which considers all eigenmodes of the structure and d
 etermines the fastest growing one\, thus selecting the corresponding wavel
 ength as the critical one that pertains to the structure’s failure mode.
  This method of analysis is meaningful only when the velocity of material 
 points in the perfect structure is significantly lower than the associated
  characteristic wave propagation speeds. The novel idea proposed here is t
 o analyze the time-dependent response to perturbations of the transient (h
 igh strain rates) states of these structures\, in order to understand the 
 initiation of the corresponding failure mechanisms. \nThree examples will 
 be presented: the first pertains to axially strained bars\, motivated by t
 he experimental studies of [1] on the high strain rate extension of thin r
 ings\, that show no evidence of a dominant wavelength in their failure mod
 e and no influence of strain-rate sensitivity on the necking strains. In t
 he interest of analytical tractability\, we study the extension of a 1D in
 compressible\, nonlinearly elastic bar at different strain rates by follow
 ing the evolution of localized small perturbations introduced at different
  times. \nThe second example deals with an externally pressurized ring\, a
  structure that is already unstable under static loading. Experiments on e
 lectromagnetically compressed rings by [2] show an irregular failure patte
 rn with no dominant wavenumber\, in contrast to the static case where an e
 llipsoidal mode is the critical one at the onset of bifurcation. The ring
 ’s stability is studied by following the evolution of a localized small 
 perturbation. For small values of the applied loading rate\, the structure
  fails through a global mode\, while for large values of the applied loadi
 ng rate the structure fails by a localized mode of deformation. \nThe thir
 d example consists of a thin elasto-plastic membrane under rapid biaxial s
 tretching. A perturbation is placed at the center of the sheet and its sta
 bility is studied by following the time-evolution of this perturbation. Fo
 r as long as the sheet has not reached conditions of loss of ellipticity\,
  the amplitude of perturbation decays with time\, indicating that the shee
 t is dynamically stable. By investigating the times associated with the on
 set of loss of ellipticity along a particular propagation direction and wi
 th the loss of ellipticity along all possible propagation directions\, one
  can establish influence zones for a localized perturbation. Similar techn
 iques can also estimate the ductility increase in a sheet by studying the 
 time necessary for the signal of a perturbation to reach the sheet’s bou
 ndary. These results have been calculated for a number of different elasto
 -plastic constitutive laws.\n\nWork in collaboration with: K. Ravi-Chandar
 \, T. Putelat and G. Wen\n\n [1] Zhang\, H. and Ravi-Chandar\, K. (2006). 
 On the dynamics of necking and fragmentation – I. real-time and post-mor
 tem observations in al 6061-O. International Journal of Fracture\, 142:183
 –217.\n\n [2] Mainy\, A. (2012). Dynamic buckling of thin metallic rings
  under external pressure. Master’s thesis\, University of Texas.\n
LOCATION:Oatley Seminar Room\, Department of Engineering
END:VEVENT
END:VCALENDAR