Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables

This is the first part of an effort to connect molecular dynamics to a well-established continuum theory, micromorphic theory. This effort includes two parts: mechanical variables and balance laws. In this paper, the physical picture of micromorphic theory is introduced. A geometric model of an atomic system is presented. The microscopic expressions of all the instantaneous mechanical variables in micromorphic theory are derived and related to atomic coordinates and velocities, and the corresponding continuum field quantities are obtained through statistical ensemble average. The link between the two thoroughly different models is analytically established.