Homogenization technique

Hello all,

Why is there no body force considered in the equilibrium equations of the RVE in the homogenization technique?

The overall response of the RVE is obtained by solving the RVE boundary value problem under prescribed boundary conditions (either traction or displacement BC) without considering the body force.

This is an extract from Sia Nemat-Nasser & Muneo Hori book: microstructure: overall properties of heterogeneous materials  ,2nd Edition, pp 19 : "The balance equations contain the body forces representing the effect of the materials not in contact with the considered continuum and the inertia forces due to the motion of the continuum itself, as well as the associated force and displacement boundary data which represent the effect of the other continua in contact with the considered continuum. Therefore, in formulating boundary-value problems associated with an RVE, it is not necessary to include the body forces."

Could you please explain to me  the above in your own words.

Thanks,

This can be understood as

This can be understood as the overall effects of the body force are included in the macroscopic equations governing the homogenized medium.

Re. Body forces and homogenization

That statement is true only for quasistatic situations.  For homogenization in dynamic situations you do need the body force for uniqueness.  See, for example,

and

-- Biswajit