It should be noted that the virtual displacement    is any arbitrary displacement. It can be chosen to vary on macroscopic or microscopic level. If we choose    to vary only on macroscopic level and be a constant on microscopic level then we get the macroscopic equilibrium equation as

(7.137)

Here,   for the chosen variation of virtual displacement. However, if we choose    to vary only on microscopic level and be a constant on macroscopic level then we get the microscopic equilibrium equation as

(7.138)

Here,    for the chosen variation of virtual displacement. Since    varies periodically, Equation (7.137) and Equation (7.138) may be simplified assuming  approaching zero in the limit as

(7.139)

and

(7.140)

Equation (7.140) to be true, the integration term over the RVE should be zero. This leads to the following condition:

(7.141)

Here, in general, the strain    is not known. However, for a linear problem, any arbitrary    can be written as linear combination of unit strains as given in the following equation. The unit strains in the following equation are given for 3D case.