  Using multiple scattering theory, we derived for the first time analytical
formulas for electrostrictive tensors for two dimensional metamaterial systems.
The electrostrictive tensor terms are found to depend explicitly on the
symmetry of the underlying lattice of the metamaterial and they also depend
explicitly on the direction of a local effective wave vector. These analytical
results enable us to calculate light induced body forces inside a composite
system (metamaterial) using the Helmholtz stress tensor within the effective
medium formalism in the sense that the fields used in the stress tensor are
those obtained by solving the macroscopic Maxwell equation with the
microstructure of the metamaterial replaced by an effective medium. Our results
point to some fundamental questions of using an effective medium theory to
determine optical force density. In particular, the fact that Helmholtz tensor
carries electrostrictive terms that are explicitly symmetry dependent means
that the standard effective medium parameters cannot give sufficient
information to determine body force density, even though they can give the
correct total force. A more challenging issue is that the electrostrictive
terms are related to a local effective wave vector, and it is not always
obtainable in systems with boundary reflections within the context of a
standard effective medium approach.
