Generalized expression of macroscopic stress and balance equations of micromorphic continuum based on lattice dynamics

In previous papers, microscopic expression of stress and balance equations for a solid which has a simple lattice were described with the microscopic values in the mesodomain without an assumption of a constrained gradient. In this paper, the solid is remodeled as an assembly of atoms which are arranged randomly. Microscopic expressions of stress, higher-order stress and heat flux are newly discussed expressing the equilibrium conditions for the tetrahedral element in the mesodomain. Stress is represented as an area averaged values with microscopic quantities such as interatomic potential, body force, inertia force and fabric vectors related to the configuration of atoms in the mesodomain. Balance laws of momentum and moments of momentum are derived on the basis of the equations of the motion of atoms. The energy equation is described with the averaged values over the domain dividing the velocity of an atom into the macroscopic motion and thermal motions.