变形色散固体中的非线性横波
Nonlinear transverse waves in deformed dispersive solids
摘要：
我们提出了一个唯象的方法，在非线性弹性色散。提出了一个简单的，热力学的声音，本构模型来描述（非耗散）性能的超弹性分散固体，而不求助于一个微观结构或特殊的几何形状。结果，非线性和色散波可以在这种固体中传播，并出现特殊的波，一些经典的（无限延伸的周期波或脉冲孤立波），一些奇异的（紧支撑的扭结或脉冲波）。我们证明，对于不可压缩色散幂律固体和四阶弹性固体，孤立波只能在线性横向极化的情况下存在。我们还研究了预拉伸和硬化的影响。我们提供与其他（准连续，渐近）理论的链接，特别是，一个适当的渐近多尺度扩展专门我们的精确运动方程的矢量MKdV方程，任何超弹性材料。
英文摘要：
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without recourse to a microstructure or a special geometry. As a result, nonlinear and dispersive waves can travel in the bulk of such solids, and special waves emerge, some classic (periodic waves or pulse solitary waves of infinite extend), some exotic (kink or pulse waves of compact support). We show that for incompressible dispersive power-law solids and forth-order elasticity solids, solitary waves can however only exist in the case of linear transverse polarization. We also study the influence of pre-stretch and hardening. We provide links with other (quasi-continuum, asymptotic) theories; in particular, an appropriate asymptotic multiscale expansion specializes our exact equations of motion to the vectorial MKdV equation, for any hyperelastic material.
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