TY - JOUR
T1 - Global structure stability for the wave catching-up phenomenon in a prestressed two-material bar
AU - Huang, Shou-Jun
AU - Dai, Hui-Hui
AU - Kong, De-Xing
PY - 2015
Y1 - 2015
N2 - Shock waves in a structure can result in the detachment of an interface and induce microcracks. In a recent study [Huang et al., R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 468 (2012), pp. 3882-3901], it was shown that for certain nonlinearly elastic materials it is possible to generate a phenomenon in which a tensile wave can catch the first transmitted compressive wave (so the former can be undermined) in an initially stress-free two-material bar. In this study, we consider the wave catching-up phenomenon in a nonlinearly elastic prestressed two-material bar. We use the same method as that used by Huang et al. in the previously mentioned paper to construct solutions. Our main focus is on proving the global structure stability of the solutions in a prestressed (or initially stress-free) two-material bar. We first reduce the corresponding initial boundary value problem into several typical free boundary problems based on the formulation of Riemann invariants. Then, using a constructive method and carefully treating the complexity arising from multiple reflections of waves at the interface in the two-material bar, we successfully prove the global structure stability of the wave catching-up phenomenon.
AB - Shock waves in a structure can result in the detachment of an interface and induce microcracks. In a recent study [Huang et al., R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 468 (2012), pp. 3882-3901], it was shown that for certain nonlinearly elastic materials it is possible to generate a phenomenon in which a tensile wave can catch the first transmitted compressive wave (so the former can be undermined) in an initially stress-free two-material bar. In this study, we consider the wave catching-up phenomenon in a nonlinearly elastic prestressed two-material bar. We use the same method as that used by Huang et al. in the previously mentioned paper to construct solutions. Our main focus is on proving the global structure stability of the solutions in a prestressed (or initially stress-free) two-material bar. We first reduce the corresponding initial boundary value problem into several typical free boundary problems based on the formulation of Riemann invariants. Then, using a constructive method and carefully treating the complexity arising from multiple reflections of waves at the interface in the two-material bar, we successfully prove the global structure stability of the wave catching-up phenomenon.
KW - Global structure stability
KW - Impact
KW - Prestress
KW - Two-material bar
KW - Wave catching-up phenomenon
UR - http://www.scopus.com/inward/record.url?scp=84928996661&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84928996661&origin=recordpage
U2 - 10.1137/130920265
DO - 10.1137/130920265
M3 - RGC 21 - Publication in refereed journal
VL - 75
SP - 585
EP - 604
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 2
ER -