Stress distributions in an elastic body due to molecular interactions considering one-dimensional periodic material distribution based on Mindlin’s solution
Stress distributions in an elastic body due to molecular interactions considering one-dimensional periodic material distribution based on Mindlin’s solution
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DOI：
10.1007/s00542-019-04537-6
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
H. Matsuoka;T. Otani;S. Fukui
中科院分区：
文献类型：
--
作者：
H. Matsuoka;T. Otani;S. Fukui
基于Mindlin解，建立了一种计算分子相互作用引起的半无限弹性体应力分布的方法。考虑材料在平面内即x方向上的一维周期性分布，由Lennard-Jones势导出的分子相互作用力作为Mindlin溶液中的集中力。作为材料周期性分布的典型例子，计算了作用在（100）和（001）表面上的应力（σx，σz和τzx）。用彩色图表示应力分布，定量地阐明了应力分布的基本特征，特别是表面距离的影响。解析导出了离表面较远位置的σx、σz、τ zx3个渐近值。σ xx和σ zx的值相同，取决于表面距离，而τzx的值总是零。这种差异来自于非波动贡献的存在。
A method to calculate the stress distributions in a semi-infinite elastic body caused by molecular interactions has been established based on Mindlin’s solution. A molecular interaction force derived from the Lennard-Jones potential considering a one-dimensional periodic material distribution in the in-plane direction, i.e.,x-direction, was used as a concentrated force in Mindlin’s solution. The stresses acting on the (100) and (001) surfaces (σx,σz, andτzx) for the distribution of two materials were calculated as a typical example of a periodic material distribution. The stress distributions were shown by color maps and the basic characteristics of the stress distribution, especially the effects of the surface distance, were quantitatively clarified. The asymptotic values ofσx,σz, andτzxat the position far from the surface were analytically derived. Those ofσxandσzhad the same value, depending on the surface distance, while that ofτzxwas always zero. This difference comes from the existence of a non-fluctuation contribution.