  We study the large-scale behavior of a small-strain lattice model for a
network composed of elastoplastic springs with random material properties. We
formulate the model as an evolutionary rate independent system (ERIS). In an
earlier work we derived a homogenized continuum model, which has the form of
linearized elastoplasticity, as evolutionary $\Gamma$-limit as the lattice
parameter tends to zero. In the present paper we introduce a periodic
representative volume element approximation (RVE) for the homogenized system.
As a main result we prove convergence of the RVE approximation as the size of
the RVE tends to infinity. We also show that the hysteretic stress-strain
relation of the effective system can be described with help of a generalized
Prandt-Ishlinskii operator, and we prove convergence of a periodic RVE
approximation for that operator. We combine the RVE approximation with a
numerical scheme for rate-independent systems and obtain a computational scheme
that we use to numerically investigate the homogenized system in the specific
case when the original network is given by a two-dimensional lattice model. We
simulate the response of the system to cyclic and uniaxial, monotonic loading,
and numerically investigate the convergence rate of the periodic RVE
approximation. In particular, our simulations show that the RVE error decays
with the same rate as the RVE error in the static case of linear elasticity.
