A Study of Deformation and Stress-Strain Distribution of Nano-scale Rod under Bending Load by Molecular Dynamics and FEM

以分子動力學與有線元素法於奈米級棒材彎曲之彈變行為與應力－應變分布之研究

林榮慶(Zone-Ching Lin) ； 趙彥傑(Jen-Ching Huang) ； 黃仁清(Yen-Chieh Chao)

《中國機械工程學刊》 29卷1期 (2008/02) Pp. 1-11

https://doi.org/10.29979/JCSME.200802.0001

摘要

本文以分子動力學探討奈米級銅薄膜在彈性範圍內的彎曲受力的行為。本文將原子視為元素節點，以分子動力學求解出原子的位移，利用形狀函數觀念求解出元素各軸向應變及等效應變，再利用有限元素法之彈性應力－應變構成方程式求出各元素之各軸向應力值與等效應力，再進而算出原子之各軸向應變、應力及等效應變應力，並計算受力層三軸向之作用力，以了解元件受力時，每個區域的應變與應力分佈情形，進而分析其中之關鍵因素。並提出在二段式修正模式下，藉由微調剛體位移層X軸方向的位移，來補償由剛體位移層下降模式所造成的X軸力量誤差。

並列摘要

In this article, we use molecular dynamic to simulate the copper nano-scale rod during bending. We use molecular dynamic to match the CST concept with finite element analysis method. First of all, we define atoms as nodes, which obtain the displacements of atoms in the simulation. Second, use the CST concept to obtain the strain of each element in three axial. Third, we use the elastic stress-strain function with finite element analysis method to calculate the stress of each element in three axial. Finally, we use the strain and stress of each element to calculate the strain and stress of each atom in three axial. Therefore, we can use the values of the strains and stresses mentioned above to understand the strains and stresses contour distributions in each section of the model and to compare the difference of the distributions with the macro phenomenon when the models were loaded. We calculate the force of x-, y-and z-axial in the rigid body layer of this model. And this paper proposed a two-step correction model, through the slight adjustment of displacement in X-axis direction at the rigid body displacement layer, the X-axis force error caused by the descending model at the rigid body displacement layer can be compensated. The result of this study helps us to understand the elastic stress-strain behavior of the model and indicates an important basic and new direction on the elastic field for nano-scale elements.

並列關鍵字

Molecular dynamics ； Finite element method ； Bending ； Nano-scale thin film ； Stress-strain behavior