Admissible deformation fields for the homogenization of elastoplastic materials with generalized periodicity

•We present a new functional setting for the two-scale homogenization of elastoplastic materials exhibiting generalized periodicity.•All micro- and macro-deformation functions, their relations and their properties are shown.•The above setting and properties, as well as all constitutive equations, are proved by passing to the two-scale convergence limit in the heterogeneous problem.

In this paper we present the admissible deformation fields and the corresponding functional setting needed for the homogenization of the non-linear equations describing the elastoplastic behavior of structures with generalized periodicity.