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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Dissipation at a shock wave in an elastic bar - Pr
ashant Purohit (University of Pennsylvania)
DTSTART;TZID=Europe/London:20221208T113000
DTEND;TZID=Europe/London:20221208T120000
UID:TALK183803AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/183803
DESCRIPTION:Propagating discontinuities in continua\, such as\
, shocks and phase transition fronts often cause d
issipation. The dissipated energy is said to manif
est in high frequency oscillations behind the prop
agating front\, yet there is no quantitative accou
nting of it. In this talk we relate the energy dis
sipated at a shock wave in a non-linearly elastic
bar to the energy in the oscillations in two relat
ed dissipationless\, dispersive systems. We study
three one-dimensional dynamic impact problems. Pro
blem 1 concerns a nonlinearlu elastic bar. Problem
2 a discrete chain of particles\, and Problem 3 a
continuum with a strain-gradient term in the cons
titutive relation. In the impact problem considere
d the free boundary of each initially quiescent bo
dy is subjected to a sudden velocity\, that is the
n held constant for all subsequent time. There is
energy dissipation at the shock in Problem 1\, but
Problems 2 and 3 are conservative. Problem 1 is s
olved analytically\, Problem 2 numerically and an
approximate solution to Problem 3 based on dispers
ive shock waves is constructed analytically. The r
ate of increase in the oscillatory energy in Probl
ems 2 and 3 are calculated and compared with the d
issipation rate at the shock in Problem 1. The res
ults indicate that the former is a good qualitativ
e measure of the latter. The quantitative agreemen
t is satisfactory at larger impact speeds but less
so at smaller speeds\, some reasons for which are
discussed.\nJoint work with Rohan Abeyaratne\, Ma
ssachusetts Institute of Technology\, Cambridge\,
USA.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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