An isotropic dynamically consistent gradient elasticity model derived from a 2D lattice
An isotropic dynamically consistent gradient elasticity model derived from a 2D lattice
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从二维晶格导出的各向同性动态一致梯度弹性模型
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
H. Askes
中科院分区：
文献类型：
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作者：
A. Metrikine;H. Askes
本文给出了从二维格点导出二阶各向同性连续介质的方法。导出的连续介质是各向同性和动态一致的，在这个意义上，它是无条件稳定的，并禁止无限的能量传播速度。连续体的拉格朗日密度由基础晶格的拉格朗日函数得到。该密度用于获得与连续体运动方程直接对应的标准和高阶应力的表达式。导出的连续体的特征在于两个额外的参数相对于经典的弹性连续体。这些是特征的长度尺度和无量纲的连续化参数，间接表征的时间尺度的派生连续。从稳定性分析中发现后一个参数的裕度。可以设想的是，连续化参数可以采用沿连续体表面沿着传播的高频脉冲来测量。本文从理论上研究了这种脉冲的激发和传播。
This paper presents a derivation of a second-order isotropic continuum from a 2D lattice. The derived continuum is isotropic and dynamically consistent in the sense that it is unconditionally stable and prohibits the infinite speed of energy propagation. The Lagrangian density of the continuum is obtained from the Lagrange function of the underlying lattice. This density is used to obtain the expressions for standard and higher-order stresses in direct correspondence with the equations of the continuum motion. The derived continuum is characterized by two additional parameters relative to the classical elastic continuum. These are the characteristic lengthscale and a dimensionless continualization parameter, which characterizes indirectly the timescale of the derived continuum. The margins for the latter parameter are found from the stability analysis. It is envisaged that the continualization parameter could be measured employing a high-frequency pulse propagating along the surface of the continuum. Excitation and propagation of such pulse is studied theoretically in this paper.