Microscopic expressions of stress and higher-order stresses in metals based on lattice dynamics

The essence of macroscopic quantities in solid mechanics can be grasped by expressing these quantities with kinematic and mechanical quantities of atoms. In this paper, a method is proposed to obtain the microscopic expressions of macroscopic quantities.The concept of mesodomain is introduced in macroscopic materials so that the kinematic and mechanical quantities of atoms are averaged in this domain.The domains are associated with these averaged values and are regarded as infinitesimal elements of continua.Macroscopic balance equations and boundary conditions not only for stress but also for higher-order stresses are derived by using the principle of virtual power described with the above averaged values. The stress and higher-order stresses are expressed with the microscopic quantities which can be obtained from the molecular dynamics.