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计算数学  2020, Vol. 42 Issue (3): 279-297    DOI:
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基于分子动力学模拟的金属构件的弹-塑性分解方法
崔俊芝, 余翌帆
LSEC, ICMSEC, 中国科学院数学与系统科学研究院, 北京 100190;中国科学院大学数学科学学院, 北京 100049
ELASTIC-PLASTIC DECOMPOSITION METHOD OF METALLIC STRUCTURE BASED ON MOLECULE DYNAMICS SIMULATION
Cui Junzhi, Yu Yifan
LSEC, ICMSEC, Academy of Mathematics and Systems Science, CAS, Beijing 100190, China;School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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摘要 针对金属多晶材料构件的分子动力学(MD)模拟,本文提出了一种新的弹-塑性分解方法.文章将MD运动轨迹分解为结构变形和热振动,给出了计算结构变形的方法和近似公式;针对金属多晶材料构件的当前构型,给出了基于FCC|BCC晶胞和四原子占位的四面体单元相组合的连续变形函数及计算变形梯度的算法;利用原子-连续关联模型,发展了计算当前构型应力场和弹性张量的算法.分析了当构件承受过大载荷后在材料内部所产生的微观缺陷,并将其分类标定为位错、层错、挛晶界、晶界和空位等;对于层错和挛晶界讨论了在弹性卸载过程中应满足的刚体运动约束方程;利用极小势能原理构造了基于当前构型的弹性卸载算法,进而给出了完整的基于MD模拟的计算弹-塑性应变的算法.最后,针对单晶铜纳米线拉伸的MD模拟,计算了弹-塑性应变场,验证了本文方法的合理性.
本文提出的基于MD模拟的弹-塑性分解方法,为从微观到宏观的多尺度和多模型耦合计算提供了算法支撑.
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关键词分子动力学模拟   结构变形   弹-塑性分解   极小势能原理   弹性卸载算法     
Abstract: In this paper a new elastic-plastic strain decomposition method is proposed based on Molecule Dynamics(MD) simulation for metallic structures. First the motion traces of atoms are decomposed into structural deformation component and thermal vibration, then the computational method and approximate formulae on the structural deformation are given. To the current configuration of the structure the continuous deformation functions are constructed based on the composition pattern of BCC|FCC cells and tetrahedral elements supported by 4-atoms, and the algorithm of deformation gradient is shown. And by using the atomic-continuum coupled model the calculation formulae of the stress fields and elasticity tensor are developed. And then, the micro-defect forms generated by overlarge loading inside materials are analyzed, and classified into dislocations, stacking faults, twin boundaries, grain boundaries and vacancies et al. The constrained equations of rigid body motion satisfied for the stacking faults and twin boundaries during the elastic unloading process are derived, then the elastic unloading algorithm of current configuration is created by making use of minimum potential energy principle. Further, the entire elastic-plastic strain decomposition algorithm based on MD simulation is proposed. Finally, the numerical results for the tension of single crystal Cu nanowire are shown. It shows that the elastic-plastic strain decomposition method in this paper is reasonable.
The elastic-plastic decomposition method based on MD simulation presented above can be applied into the multi-scales analysis coupled with multiple models for mechanic behaviors of materials and their structures.
Key wordsMolecule dynamics simulation   Structural deformation   Elastic-plastic strain decomposition   Minimum potential energy principle   Elastic unloading algorithm   
收稿日期: 2020-03-10;
基金资助:

国家自然科学基金重点项目(51739007)资助.

引用本文:   
. 基于分子动力学模拟的金属构件的弹-塑性分解方法[J]. 计算数学, 2020, 42(3): 279-297.
. ELASTIC-PLASTIC DECOMPOSITION METHOD OF METALLIC STRUCTURE BASED ON MOLECULE DYNAMICS SIMULATION[J]. Mathematica Numerica Sinica, 2020, 42(3): 279-297.
 
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