基于原子模型的非局域连续模型  

A nonlocal continuum model based on atomistic model

作　　者：向美珍[1] 崔俊芝[1] 田霞[1] 

机构地区：[1]中国科学院数学与系统科学研究院,计算数学与科学工程计算研究所,科学与工程计算国家重点实验室,北京100190

出　　处：《中国科学：物理学、力学、天文学》2011年第3期292-301,共10页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:90916027);国家重大基础研究计划(批准号:2010CB832702);科学和工程计算国家重点实验室资助项目

摘　　要：在传统的连续模型中,本构关系,例如胡克定律、热传导的傅立叶定律是宏观现象的表征.在原子尺度下,传统连续模型具有很大的局限性,其中一个原因就是传统连续模型忽略了原子间相互作用的非局域性.本文在不采用任何经验的本构假设和局部均匀变形假设(如Cauchy-Born假设)的情况下,严格基于原子模型,构造了一个连续模型,将原子间相互作用力的非局域性和非线性性自然地嵌入到模型中.此模型可以有效表现原子尺度的非均匀变形.In traditional continuum theories,constitutive relations such as generalized Hooke’s law and the Fourier law for heatconduction,are representations of macroscopic phenomenons.These theories have severe limitations as the length scaleof the structure becomes close to the atomistic dimensions.The failure of the traditional continuum theories at atomisticscale can be attribute to the ignoring of the length scale induced by intrinsic non-locality of atomistic interactions.Theprimary objective of this work is to construct a coupled atomistic-continuum model strictly based on the atomistic modelbypassing any empirical constitutive law and any local homogeneous assumption such as Cauchy-Born rule.The intrinsicnon-locality of the atomistic interactions are explicitly built into the model.Inhomogeneous deformation at atomistic scalecan be efficiently represented by this model.

关 键 词：原子模型 推广连续模型 多尺度 非局域性 

分 类 号：O562[理学—原子与分子物理]