Propagation of acceleration waves in incompressible saturated porous solids

Within the framework of the incompressible porous media model, the propagation properties of acceleration waves in liquid-filled porous solids is discussed. The incompressibility of the two constituents in the model forces the amplitudes of the longitudinal waves in the skeleton and in the liquid to satisfy a certain relation. The two propagation speeds are presented by examination for the existence of acceleration waves and only longitudinal and transverse waves are realizable in the incompressible two-phase porous materials.     

Finite and symmetric thermomechanical waves in materials with internal state variables

The paper is devoted to the study of wave propagation through materials with internal state variables under two main assumptions: finite speed of propagation and symmetry of acceleration waves. Additional constitutive assumptions are also used: heat flux does not depend on the temperature gradient and the time-derivatives of internal state variables are linear functions of the temperature gradient. Under all these hypotheses, in the neighborhood of a strong equilibrium state, one finds four real and symmetric possible acceleration waves, at least two of them being coupled waves, and heat flux results an internal state variable. All these results are obtained in the general three-dimensional case. As an illustration, the isotropic linear theory is considered, where both acceleration and shock waves are treated.     

Thermodynamic restrictions and wave features of a non-linear Maxwell model

A non-linear rate-type constitutive equation, established by Rajagopal, provides a generalization of the Maxwell fluid. This note embodies such a constitutive equation within the scheme of materials with internal variables thus allowing also for solids with both dissipative and thermoelastic mechanisms. The compatibility with the second law of thermodynamics, expressed by the Clausius–Duhem inequality, is examined and the restrictions on the evolution equations are determined. Next the propagation condition of discontinuity waves is derived, for shock waves and acceleration waves, by regarding the body as a definite conductor. Infinitesimal shock waves and acceleration waves show similar effects. The effective acoustic tensor proves to be the sum of a thermoelastic tensor and a tensor arising from the rate-type equation.     

Acceleration wave speeds in a hypoplastic constitutive model

The paper presents a theoretical investigation of acceleration waves in a plastic material described by an incrementally non-linear hypoplastic constitutive equation. Speeds of plane acceleration waves and their dependence on the stress state are calculated. The spectrum of possible wave speeds is found to be continuous, which is in contrast to discrete wave speed spectra in incrementally linear models. Two types of ill-posedness are revealed, known as flutter ill-posedness and stationary discontinuity. The wave speed analysis is also performed by the characteristic method, leading to different equations compared to the acceleration wave approach. It is proved that for the considered hypoplastic constitutive equation both approaches give identical wave speed spectra.     

Acceleration waves in constrained elastic materials

Well known results on the propagation and growth of acceleration waves in Cauchy elastic materials are extended to materials which suffer one or two internal constraints. It is proved, under certain restrictions, that acceleration waves will not propagate in a material which has three or more internal constraints. The great simplifications deriving from an assumption of hyperelasticity are indicated. The present results could be extended to materials other than simple elastic.     

The phase configuration of the waves around an accelerating disturbance in a rotating stratified fluid

Ray theory is extended to consider the case of an accelerating disturbance which is producing waves in a rotating stratified fluid. Starting from the equations of motion, dispersion relations are derived for surface gravity waves, capillary waves, Rossby waves and internal-inertial waves. The wave system is studied in each case for the problem of a body starting impulsively from rest and for a body starting from rest and moving with constant acceleration.     

Simple waves in general elastic materials

The general theory of simple waves in Green-elastic and Cauchy-elastic materials is given. Such waves generate three-dimensional unsteady deformations. Boundary conditions producing such waves are derived together with conditions under which shocks occur. The theory is used to illustrate conditions behind acceleration fronts moving into homogeneously deformed regions and also the modes of propagation of fronts moving into a simple wave. The steady flow of an elastic material past a rigid developable surface is discussed. Simple waves which are principal waves are also discussed.     

Behaviour of the acceleration and shock waves in materials with internal state variables

The explicit expressions for the change in the amplitudes of one-dimensional acceleration and shock waves propagating through arbitrary homogeneous materials described by the strain and internal state variables/parameters/are derived. The existence of a critical amplitude β for the acceleration wave and a critical strain gradient λ for the shock wave is established. For an infinitesimal shock wave the general form of the solution of the governing differential equation is furnished. The differential equations for the amplitudes of these two kind of waves are applied to an elastic-viscoplastic material.     

On the universality of nonthermal electron acceleration due to quasi-turbulent wakefields

Nonthermal acceleration of relativistic electrons in a wakefield induced by large amplitude light waves is discussed. It is considered that large amplitude light waves are excited as the precursor waves in the upstream of relativistic perpendicular shocks in the universe, and that the wakefield is excited by the light ponderomotive force. Thus, the wakefield acceleration is possible in the astrophysical circumstances. We model such shock environments in a laboratory plasma by substituting an intense laser pulse for the large amplitude light waves. By performing 2-D particle-in-cell simulations, we discuss the properties of the wakefield acceleration in various laser and plasma conditions. With the relativistic intensities of the laser pulses, the electrons are nonthermally accelerated by the wakefield. When the pulse length and the spot size are comparable to the electron inertial scale, the energy distribution functions of the electrons can be monoenergetic. On the other hand, when the pulse spatial scales are much larger than the electron inertial scale, which occurs in the case of the shock precursor light waves, the distribution functions are universally represented by power law spectra with an index of 2, independent of the laser intensity, the plasma density, and the laser pulse size.     

Modelling solitons under the hydrostatic and Boussinesq approximations

An examination of solitary waves in 3D, time‐dependant hydrostatic and Boussinesq numerical models is presented. It is shown that waves in these models will deform and that only the acceleration term in the vertical momentum equation need be included to correct the wave propagation. Modelling of solitary waves propagating near the surface of a small to medium body of water, such as a lake, are used to illustrate the results. The results are also compared with experiments performed by other authors. Then as an improvement, an alternative numerical scheme is used which includes only the vertical acceleration term. Effects of horizontal and vertical diffusion on soliton wave structure is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Acceleration waves in rate type plastic material with general work-hardening

The acceleration waves propagating in the rate type plastic material are investigated, where the material has isotropic and kinematic work-hardening. The waves are classified into unloading and loading waves, and have, in general, different propagation velocities. The propagation velocities of the principal waves are obtained for the Prandtl-Reuss material and the T material.     

爆炸地震波模拟研究

基于能够描述爆炸地震波的非平稳随机过程模型进行爆炸地震波的模拟研究。基于爆炸地震能量守恒以及经验关系,提出了能够考虑装药量和爆距影响的爆炸地震波功率谱密度和幅值包络线模型,并且利用实测的爆炸试验数据,对模型参数进行标定,给出单点、两点（微差）和多点（微差）爆炸地震波实用模拟方法。结果表明模拟得到的爆炸地震波时程能够很好地再现爆炸地震波的一些特性。     

Acceleration waves and stability

A method to examine the stability in case of weak discontinuity waves (acceleration waves) propagating in isotropic media in which mechanical relaxation phenomena occur is used in the case of non linearity. An upper bound for the initial distribution density is obtained.     

The influence of constraints on the properties of acceleration waves in isotropic thermoelastic media

The properties of acceleration waves are investigated for situations in which the waves propagate in isotropic heat-conducting elastic media subject to arbitrary sets of constraints. Conditions under which waves may exist in the presence of constraints are investigated for classes of constraints broad enough to encompass all those encountered in practice. Attention is focussed on principal waves, and results are presented for the growth of the amplitudes of such waves first for fronts of arbitrary curvature, and subsequently by specialisation for plane, cylindrical and spherical waves travelling in material which has undergone one-dimensional plane deformation, cylindrically symmetric and spherically symmetric deformation, respectively.     

Instabilities in elastic–plastic fluid-saturated porous media: harmonic wave versus acceleration wave analyses

A linearized analysis of the stability of the flow in elastic–plastic fluid-saturated porous media with incompressible constituents is performed. A relationship is established between the results of this analysis and the results of analyses based on acceleration waves performed by Loret and Harireche [Journal of the Mechanics and Physics of Solids 39, 569–606 (1991) ] and by Loret et al. [International Journal of Solids and Structures 34, 1583–1608 (1997) ]; a justification is found for the growth of the acceleration waves in the non-associative case when their speeds are real and a clarification is provided relative to the growth or decay of waves in the interior of flutter regions.     

爆炸载荷下板条边界斜裂纹的动态扩展行为

为了研究爆炸应力波作用下板条边界斜裂纹的动态扩展行为,首先分析了爆炸应力波在含边界斜裂纹板条中的传播,其次采用动态焦散线实验方法,进行了爆炸载荷下板条边界斜裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界斜裂纹的扩展过程中,裂纹扩展速度、扩展加速度和裂尖动态应力强度因子随时间波动变化,扩展速度最大值...     

Effect of initial deformations on wave front propagation in anisotropic plates

The effects of large amplitudes and initial deformations on shock waves and acceleration waves propagating in fiber-reinforced laminated plates are investigated. Three cases are discussed, namely the large amplitude shock under initial in-plane deformations, small amplitude waves under in-plane deformations, and small amplitude waves propagating in a plate with large deflection. It is found that the in-plane force has a substantial effect on the transverse shear mode but little effects on other modes. The large initial deflection, however, is found to have considerable effects on all modes. A general procedure for constructing the wave surfaces is also presented.     

Decay of acceleration waves in elastic rods

The problem of the propagation and decay of acceleration waves in nonlinear hyperelastic rods is treated herein. The general growth-decay law governing wave strength is obtained for all waves which can propagate in the rod. An expression for the induced higher order wave is also obtained. The forms taken by the law of growth or decay in a number of special cases are given.     

Existence and interaction of acceleration wave with a characteristic shock in transient pinched plasma

In this paper, the evolution of an acceleration wave and a characteristic shock for the system of partial equations describing one dimensional, unsteady, axisymmetric motion of transient pinched plasma has been considered. The amplitude of the acceleration wave propagating along the characteristic associated with the largest eigenvalue has been evaluated. The interaction of the acceleration wave with the characteristic shock has been investigated. The amplitudes of the reflected and transmitted waves and the jump in the shockwave acceleration after interaction are evaluated.     

Acceleration waves in a two-phase solid-gas flow

An analysis of the propagation of acceleration waves is performed for a solid-gas flow in adiabatic or isothermal cases. The flow considered is defined by linear constitutive laws in the condition of phase separation.