The effect of long-range forces on the dynamics of a bar
The effect of long-range forces on the dynamics of a bar
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DOI：
10.1016/j.jmps.2004.08.006
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发表时间：
2005-03
影响因子：
5.3
通讯作者：
O. Weckner;R. Abeyaratne
中科院分区：
文献类型：
--
作者：
O. Weckner;R. Abeyaratne
研究了由线性微弹性材料组成的无限长杆的一维动力响应。该本构模型的主要物理特征是它考虑了长程力的影响。描述我们的设置的一般理论，包括伴随的运动方程，是由Kunin（Elastic Media with Microstructure I，1982），Rogula（Nonlocal Theory of Material Media，1982）和Silling（J. Mech. Phys. Solids 48（2000）175）独立开发的，称为周波理论。一般的初值问题的解决和运动被发现是分散的长期部队的后果。在短程力的限制下，结果收敛于线性弹性介质的经典结果。在广泛的一类特殊情况下，给出了初等形式的显式解。最引人注目的观察出现在黎曼问题对应于一个恒定的初始位移场和一个分段恒定的初始速度场。即使最初位移场是连续的，但在以后的所有时间里，它都包含一个跳跃不连续性，其拉格朗日位置保持不变。对于某些材料，不连续跳跃的幅度在平均值附近振荡，而对于其他材料，它单调增长，当它超过某个临界水平时，可能会使材料断裂。
The one-dimensional dynamic response of an infinite bar composed of a linear “microelastic material” is examined. The principal physical characteristic of this constitutive model is that it accounts for the effects of long-range forces. The general theory that describes our setting, including the accompanying equation of motion, was developed independently by Kunin (Elastic Media with Microstructure I, 1982), Rogula (Nonlocal Theory of Material Media, 1982) and Silling (J. Mech. Phys. Solids 48 (2000) 175), and is called the peridynamic theory. The general initial-value problem is solved and the motion is found to be dispersive as a consequence of the long-range forces. The result converges, in the limit of short-range forces, to the classical result for a linearly elastic medium. Explicit solutions in elementary form are given in a broad class of special cases. The most striking observations arise in the Riemann-like problem corresponding to a constant initial displacement field and a piecewise constant initial velocity field. Even though, initially, the displacement field is continuous, it involves a jump discontinuity for all later times, the Lagrangian location of which remains stationary. For some materials the magnitude of the discontinuity-jump oscillates about an average value, while for others it grows monotonically, presumably fracturing the material when it exceeds some critical level.