Bi-modular rods: Existence of supersonic shock waves

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-05-21 DOI:10.1016/j.ijnonlinmec.2025.105169

Sergey V. Kuznetsov

引用次数: 0

Abstract

It is known that the propagation of infinitesimally small harmonic elastic waves in a bi-modular rod implies the appearance of discontinuities in strain, stress and the propagation velocity. These discontinuities are known as strong shock wave fronts, or simply strong shocks. It is also known that the instantaneous velocity of the strong shocks lies in between fast and slow rod velocities of the bi-modular rod. Now, by applying the Hadamard compatibility equation for singular surfaces, it is revealed that under certain conditions the velocity of a strong shock can be infinite. This result is confirmed numerically using the hyperelastic potential for a bi-modular material and with the finite element model. It is also shown that the existence of extremely fast strong shocks implies a large local heat release.

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双模棒：超音速激波的存在

众所周知，无穷小谐波弹性波在双模杆中的传播意味着应变、应力和传播速度的不连续。这些不连续被称为强激波锋面，或简称为强激波。我们还知道，强冲击的瞬时速度位于双模杆的快杆速度和慢杆速度之间。现在，通过应用奇异表面的Hadamard相容方程，揭示了在一定条件下，强激波的速度可以是无限大的。利用双模材料的超弹性势和有限元模型对这一结果进行了数值验证。研究还表明，极快的强冲击的存在意味着大量的局部热释放。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.