EQUIVALENT CONTINUUM FOR DISCRETE MOLECULAR DYNAMIC SYSTEMS

摘要

An equivalent continuum (EC) for dynamically deforming atomistic particle systems is defined. The equivalence of the continuum to discrete atomic systems includes (ⅰ) preservation of linear and angular momenta, (ⅱ) conservation of internal, external, and inertial work rates, and (ⅲ) conservation of mass. This equivalence is achieved through the definition of (ⅰ) a continuum stress field that makes the same contribution to motion and deformation as internal interatomic forces, (ⅱ) continuum fields of body force and surface traction that make the same contribution to motion and deformation as external forces on the atoms, (ⅲ) a continuum deformation field that is work-conjugate to the continuum kinetic fields and consistent with the atomic deformation field, and (ⅳ) continuum distribution of mass that preserves the linear and angular momenta as well as kinetic energy. Construction of the continuum fields follows a process in reverse to finite element discretization. The momentum- and work-equivalence is achieved by virtue of the principle of virtual work for fully dynamic conditions. This equivalence holds for the entire system and for volume elements defined by any subset of particles in the system; therefore, averaging and characterization across different length scales are possible and size-scale effects can be explicitly analyzed. The framework of analysis provides explicit account of arbitrary atom arrangement, admitting applications to both crystalline and amorphous structures. The analysis also applies to both homogeneous materials with identical atoms and heterogeneous materials with dissimilar atoms.