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

Mi Sien; Liu Xiaoming; Wei Yueguang

doi:10.6052/0459-1879-21-449

Volume 53 Issue 11

Nov. 2021

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Chinese Journal of Theoretical and Applied Mechanics > 2021 > 53(11): 3080-3096. > DOI: 10.6052/0459-1879-21-449 CSTR: 32045.14.0459-1879-21-449

Mi Sien, Liu Xiaoming, Wei Yueguang. A transition method from discrete simulation to elastic FEA of continuous media. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 3080-3096. DOI: 10.6052/0459-1879-21-449

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

Mi Sien^{*, †},
Liu Xiaoming^*,
Wei Yueguang^**,

*.
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
†.
College of Engineering Science, University of the Chinese Academy of Sciences, Beijing 100049, China
**.
Department of Mechanics and Engineering Science, College of Engineering, BIC-ESAT, Peking University, Beijing 100871, China

Received Date: September 05, 2021
Accepted Date: October 12, 2021
Available Online: October 13, 2021

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Abstract

Abstract

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.
- molecular dynamics-finite element analysis method,
- strain/stress field,
- atom strain,
- virial stress

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