Continuum Aspect of Nanomechanics: From Micromorphic Theory to Atomistic Field Theory

作者：Wang Xianqiao^*

来源：Journal of Computational and Theoretical Nanoscience, 2011, 8(8): 1449-1466.

DOI：10.1166/jctn.2011.1835

• Micromorphic Theory
• Atomistic Field Theory
• Nanomechanics
• Molecular Dynamics

Micromorphic theory (MMT) envisions a material body as a continuous collection of deformable particles; each possesses finite size and inner structure. It may be considered as the most successful top-down formulation of a two-level continuum model, in which the deformation is expressed as a sum of macroscopic continuous deformation and internal microscopic deformation of the inner structure. To enlarge the domain of applicability of the micromorphic theory, starting from many-body dynamics and following the work of Chen and Lee (Philos. Mag. 2005), we take a bottom-up approach to rederive the generalized atomistic field theory (AFT) comprehensively and completely and establish the relationship between AFT and MMT. AFT views a crystalline material as a continuous collection of lattice points embedded within each lattice point is a group of discrete atoms. In this work, atomistic definitions and the corresponding field representations of fundamental physical quantities are introduced. The balance laws and the constitutive relations are obtained through the atomistic formulation. AFT is identical to molecular dynamics at atomic scale and can be reduced to classical continuum field theory at macroscopic scale. The application of the micromorphic theory and atomistic field theory is discussed.

• 出版日期2011-8