  To discuss the properties of metamaterials on physical grounds and to
consider them in applications, effective material parameters are usually
introduced and assigned to a given metamaterial. In most cases, only weak
spatial dispersion is considered. It allows to assign local material
properties, i.e. a permittivity and a permeability. However, this turned out to
be insufficient. To solve this problem, we study here the effective properties
of metamaterials with constitutive relations beyond a local response and take
strong spatial dispersion into account. The isofrequency surfaces of the
dispersion relation are investigated and compared to those of an actual
metamaterial. The significant improvement provides evidence for the necessity
to use nonlocal material laws in the effective description of metamaterials.
The general formulation we choose here renders our approach applicable to a
wide class of metamaterials.
