Linear analysis of Atwood number effects on shear instability in the elastic–plastic solids

Wang, Xi; Hu, Xiaoyan; Wang, Shengtao; Pan, Hao; Yin, Jian-Wei

doi:10.1038/s41598-021-96738-1

Cited by 2 publications

(4 citation statements)

References 42 publications

(40 reference statements)

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“…Growth factor are the solutions of Eq. ( 21 ) and the solving processes are similar to previous work 21 . Here, we list the dimensionless forms of the solutions.…”

Section: Growth Factor By Theorymentioning

confidence: 75%

“…The surfaces of materials are initially contact and defined by a sliding_only contact which is a two-surface method. The details of framework and reliability of the Lagrange method is performed in previous study 21 .…”

Section: Methodsmentioning

confidence: 99%

“…The mathematical formula of pressure can be obtained by integrating Eq. ( 6 ) from y = 0 to the instantaneous interface y = η ( x , t ) in y direction with C 1 = C 2 21 …”

Section: Amplitude Motion Equation By Theorymentioning

confidence: 99%

“…For the purpose of investigating surface behavior of KHI on solid, we have proposed a theoretical analysis with a potential flow method to describe the growth rate and amplitude evolution by analytical formulas 21 . The properties of resisting shear deformation of solid material influence the instability evolution of surface as flushed by tangential flow.…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamic Kelvin–Helmholtz instability on metallic surface

Wang

et al. 2023

Sci Rep

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Kelvin–Helmholtz instability on metallic surface is relevant to intense oblique impact in many physical processes such as explosive welding, Inertial Confinement Fusion and planetary impact events. Evolution of instability results in the formation of wavy morphology leading to material bonding or even mixing. However, mostly due to lack method to describe the dynamic behavior, instability mechanism controlled by elastoplastic properties of metal remains elusive. Here, we introduce a theory to reveal the evolution characteristics aroused by tangential velocity. Our simulations find that the unstable metallic surfaces exhibit amplitude growth and tangential motion by overcoming the depression of yield strength to generate wavy morphology. For diverse loading velocities, corrugated surfaces and material properties, an instability boundary distinguishes all unstable evolutions. Our analytical method with scale-independent variables reproducing numerical findings reveals plentiful characteristics of instability in strength materials. For designed loading velocities and material in oblique impact experiment in laboratory, the property of corrugated surfaces becomes an important factor to determine instability evolution.

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“…Growth factor are the solutions of Eq. ( 21 ) and the solving processes are similar to previous work 21 . Here, we list the dimensionless forms of the solutions.…”

Section: Growth Factor By Theorymentioning

confidence: 75%

Section: Methodsmentioning

confidence: 99%

“…The mathematical formula of pressure can be obtained by integrating Eq. ( 6 ) from y = 0 to the instantaneous interface y = η ( x , t ) in y direction with C 1 = C 2 21 …”

Section: Amplitude Motion Equation By Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hydrodynamic Kelvin–Helmholtz instability on metallic surface

Wang

et al. 2023

Sci Rep

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Coupled Richtmyer–Meshkov and Kelvin–Helmholtz instability on a shock-accelerated inclined single-mode interface

Cao,

Li,

Wang

et al. 2024

J. Fluid Mech.

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The coupling of Richtmyer–Meshkov instability (RMI) and Kelvin–Helmholtz instability (KHI), referred to as RM-KHI, on a shock-accelerated inclined single-mode air–SF $_6$ interface is studied through shock-tube experiments, focusing on the evolution of the perturbation distributed along the inclined interface. To clearly capture the linear (overall linear to nonlinear) evolution of RM-KHI, a series of experiments with a weak (relatively strong) incident shock is conducted. For each series of experiments, various $\theta _{i}$ (angle between incident shock and equilibrium position of the initial interface) are considered. The nonlinear flow features manifest earlier and develop faster when $\theta _{i}$ is larger and/or shock is stronger. In addition, the interface with $\theta _{i}>0^{\circ }$ evolves obliquely along its equilibrium position under the effect of KHI. RMI dominates the early-time amplitude evolution regardless of $\theta _{i}$ and shock intensity, which arises from the discrepancy in the evolution laws between RMI and KHI. KHI promotes the post-early-stage amplitude growth and its contribution is related positively to $\theta _{i}$ . An evident exponential-like amplitude evolution behaviour emerges in RM-KHI with a relatively strong shock and large $\theta _{i}$ . The linear model proposed by Mikaelian (Phys. Fluids, vol. 6, 1994, pp. 1943–1945) is valid for RM-KHI within the linear period. In contrast, the adaptive vortex model (Sohn et al., Phys. Rev. E, vol. 82, 2010, p. 046711) can effectively predict both the interface morphology and overall amplitude evolutions from the linear to nonlinear regimes.

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Linear analysis of Atwood number effects on shear instability in the elastic–plastic solids

Cited by 2 publications

References 42 publications

Hydrodynamic Kelvin–Helmholtz instability on metallic surface

Hydrodynamic Kelvin–Helmholtz instability on metallic surface

Coupled Richtmyer–Meshkov and Kelvin–Helmholtz instability on a shock-accelerated inclined single-mode interface

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