caa a22 4500 465813844 CHVBK 20180323112122.0 cr unu---uuuuu 170327e19900101xx s 000 0 eng 10.1007/BF01331800 doi (NATIONALLICENCE)springer-10.1007/BF01331800 Neck propagation as a shock wave [Elektronische Daten] [S. Kase, M. Chang] Neck propagation in the stretching of elastic solid filaments having a yield point was analyzed using the space one-dimensional thin filament governing equations developed previously by the authors and other researchers. Constitutive model for the filament was assumed to be expressible as engineering tensile stressη(X) (tensile force) given as a function of elongational strain with theη(X) curve having a yield point maxima followed by a minima and a breaking point greater than the yield point maxima. Also incorporated into the model is the hysteresis of irreversible plastic deformation. When inertia is taken into consideration, the thin filament equations were found to reduce to the nonlinear wave equation ∂2 η(X)/∂λ 2 =C 1 ∂ 2 X/∂τ 2 whereλ is Lagrangean space coordinate,τ is time, andC 1 is inertia coefficient. The above nonlinear wave equation yields a solutionX(λ, τ) having a stepwise discontinuity inX which propagates along theλ axis. The zero speed limit of the step wave solution was found to describe the above neck propagation occurring in solid filaments. Furthermore, it was recognized that the nonlinear wave equation was known for many years to also govern the plastic shock wave which propagates axially within a metal rod subjected to a very strong impact on its end. The one-dimensional atmospheric shock wave also was known to be governed by the nonlinear wave equation upon making certain simplifying assumptions. The above and other evidences lead to the conclusion that neck propagation occurring in the extension of solid filament obeying the aboveη(X) function can be formally described as a shock wave. Steinkopff, 1990 N ecking nationallicence w ave equation nationallicence f ilament extension nationallicence y ield point nationallicence s hock wave nationallicence Kase S. Kyoto Institute of Technology, Matsugasaki Sakyoku, 606, Kyoto, Japan aut Chang M. Kyoto Institute of Technology, Matsugasaki Sakyoku, 606, Kyoto, Japan aut Rheologica Acta Steinkopff-Verlag 29/1(1990-01-01), 46-59 0035-4511 29:1<46 1990 29 397 https://doi.org/10.1007/BF01331800 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01331800 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kase S. Kyoto Institute of Technology, Matsugasaki Sakyoku, 606, Kyoto, Japan aut NATIONALLICENCE 700 1- Chang M. Kyoto Institute of Technology, Matsugasaki Sakyoku, 606, Kyoto, Japan aut NATIONALLICENCE 773 0- Rheologica Acta Steinkopff-Verlag 29/1(1990-01-01), 46-59 0035-4511 29:1<46 1990 29 397 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer