一种从离散模拟到连续介质弹性模拟的过渡方法

提出了一种从离散分子动力学模拟(MD)到连续介质弹性有限元计算分析(FEA)的过渡方法, 简称MD-FEA方法. 首先通过MD计算获得晶体材料原子的移动位置, 然后根据晶体结构的周期性特征构造连续介质假设下的有限单元变形模型, 进一步结合材料的力学行为本构关系获得应变和应力场. 为了检验MD-FEA方法的有效性, 将该方法应用于详细分析Al-Ni软硬组合两相材料纳米柱体的拉伸变形问题和基底材料为Al球形压头材料为金刚石的纳米压痕问题. 采用MD-FEA方法获得了上述两种问题的应力?应变场, 并将计算结果分别与传统MD方法中通过变形梯度计算的原子应变以及原子的位力应力进行了比较, 详细讨论了用MD-FEA方法计算的应力?应变场与传统MD原子应变和位力应力的区别, 并对MD-FEA方法的有效性及其相较于传统MD方法所具有的优势进行了探讨. 结论显示, MD-FEA方法与传统MD方法在应力?应变变化平缓的区域得到的结果接近, 但在变化剧烈的区域以及材料的表/界面区域, MD-FEA方法能够得到更加精确的结果. 同时, MD-FEA方法避免了传统MD方法中, 需要人为选取截断半径以及加权函数所导致的误差. 另外, 当应变较大时, MD-FEA方法计算的小应变与传统MD方法计算的格林应变存在一定差异, 因此, MD-FEA方法更适合应变较小的情形. 

A TRANSITION METHOD FROM DISCRETE SIMULATION TO ELASTIC FEA OF CONTINUOUS MEDIA

A transition method from discrete molecular dynamics (MD) simulation to continuum elastic finite element analysis (FEA) is proposed. Firstly, the moving position and displacement of crystal material atoms is obtained by MD calculation, and then the finite element deformation model under the assumption of continuous medium is constructed according to the characteristics of crystal structure. Further, the strain and stress fields are obtained combined with the constitutive relationship of material mechanical behavior. In order to test the effectiveness of the MD-FEA method, this method is applied to analyze the tensile deformation of Al-Ni soft-hard composite nano cylinder and the nano indentation of substrate Al with spherical diamond indenter. The stress and the strain fields of the above two problems are obtained by MD-FEA method, and the calculated results are compared with the atomic strain calculated by discrete deformation gradient and the atomic potential stress in traditional MD method. The difference between the stress and strain field calculated by MD-FEA method and the traditional MD atomic strain and potential stress is discussed in detail, and the effectiveness of MD-FEA method and its advantages over traditional MD method are discussed. The result shows that the MD-FEA method and the traditional MD method are consistent when the stress and strain change softly in the volume, and in the area where stress and strain change rapidly and in the surface/interface area, the MD-FEA method can calculate the result more precise. Meanwhile, the MD-FEA method avoid the selection of the cutoff radius and weighting functions, which is necessary in traditional MD method and can lead to human error in some circumstances. When the strain is large, there are obvious difference between the small strain calculated by MD-FEA method and the Green strain calculated by traditional MD method. Thus the MD-FEA method is more suitable for the situation that the stress and strain is small.