三维弹性固体中冲击波传输方程的Lagrange描述

李永池; 丁啟财

三维弹性固体中冲击波传输方程的Lagrange描述

李永池¹,
丁啟财²

1.
合肥中国科学技术大学;
2.
美国伊利诺大学芝加哥校园

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出版历程
- 收稿日期: 1981-12-28
- 刊出日期: 1982-08-15

Lagrangian Description of Transport Equations for Shock Waves in Three-Dimensional Elastic Solids

Li Yong-chi¹,
T. C. T. Ting²

1.
University of Science and Technology of China, Hefei, Anhui;
2.
University of Illinois at Chicago Circle, Chicago, Illinois, U. S. A.

摘要

摘要: 在Lagrange坐标中导出了三维非线性弹性固体中冲击波幅度在任意传播方向上的传输方程.导出的方程说明,冲击波的幅度在任意传播方向上随时间的变化率依赖于(i)冲击波阵面紧后方介质运动的一个未知量;(ii)冲击波阵面的两个主曲率;(iii)冲击波法向波速在阵面内的表面梯度;(iv)和冲击波前方介质运动有关的非齐次项,当前方介质处于均匀运动状态时此项为零.文中指出了适当选择传播矢量以简化传输方程的几种方法.我们还得到了一组与介质本构方程无关的、联系冲击波各跳跃量变化率的普适关系.

Abstract: A set of transport equations for the growth or decay of the amplitudes of shock waves along an arbitrary propagation direction in three-dimensional nonlinear elastic solids is derived using the Lagrangian coordinates. The transport equations obtained show that the time derivative of the amplitude of a shock wave along any propagation ray depends on(i) an unknown quantity immediately behind the shock wave,(ii) the two principal curvatures of the shock surface,(iii) the gradient taken on the shock surface of the normal shock wave speed and(iv) the inhomogeneous term,which is related to the motion ahead of the shock surface, vanishes when the motion ahead of the shock surface is uniform. Several choices of the propagation vector are given for which the transport equations can be simplified. Some universal relations, which relate the time derivatives of various jump quantities to each other but which do not depend on the constitutive equations of the material, are also presented.

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参考文献(14)

[1]	Herrman,W.and Nunziato,J.W.,Nonlinear constitutive equations in Dynamic Response of Materials to Intense Impulsive Loading.ed.by P.C.chen and A.K.Hopkins,Air Force Materials Laboratory,(l972),123-281.
[2]	Chen,P.J.and Gurtin,M.E.,On the growth of one-dimensional shock waves in materials with memorg,Arch.Rat.Mech.Anal.,Vol 36,(1970),33-46.
[3]	Chen,P.J.and Gurtin,M.E.,The growth of one-dimensional shock waves in elastic nonconductors.Int.J.Solids Structures,Vol.7,(1971),5-l0.
[4]	Chen,P.J.,One-dimensional shock waves in elastic nonconductors,Arch.Rat.Mech.Anal.,Vol.43,(197l).350-360.
[5]	Ting,T.C.T.,Further study on one-dimensional shock waves in nonliear elastic media.Q.Appl.Math.,Vol.37,No.4,(1980),421-429.
[6]	Chen,P.J.and Wright,T.W.,Three-dimensional shock waves and their behaviour in elastic fluids,Mechanics,Vol.10,(1975),232-238.
[7]	Bowen,R.M.,Chen,P.J.and McCarthy,M.F.,Thermodynamic influences on the behavior of curved shock waves in elastic fluids and the vorticity jump,J.of Elasticity,Vol.6,No.4,(1976).
[8]	Wright,T.W.,An intrinsic description of unsteady shock waves,Q.J.Mech.Appl.Math.,Vol.24,(1976),311-324.
[9]	Ting,T.C.T.,Intrinsic description of the three-dimensional shock waves in nonlinear elastic fluids.Int.J.Eng.Sci.,Vol.19,(1981),629-638.
[10]	Ting,T.C.T.and Li,Y.C.,Eulerian formulation of transport equations for three-dimensional shock waves in simple elastic solids.(submitted for publication).
[11]	Truesdell,C.A.and Toupin,R.A.,The classical field theories,Handbuch der physik,Ⅲ/I,Springer,(1960) 522,711,610,645.,
[12]	McConnell,A.J.,Application of Tensor Analysis.Dover Publication,New York,(1957),197.
[13]	Bland,D.R.,On shock waves in hyperelastic media.in Second Order Effects in Elasticity and Fluid Dynamics.International Symposium,Haifa,Israel,April 23-27,ed.Markus Reiner and David Abir,(1962),93-108.
[14]	Guggenheimer,H.W.,Differential Geometry.McGraw-Hill Book Company,Inc.,New York,(1963),210．