  In complex materials, numerous intertwined phenomena underlie the overall
response at macroscale. These phenomena can pertain to different engineering
fields (mechanical , chemical, electrical), occur at different scales, can
appear as uncertain, and are nonlinear. Interacting with complex materials thus
calls for developing nonlinear computational approaches where multi-scale
techniques that grasp key phenomena at the relevant scale need to be mingled
with stochastic methods accounting for uncertainties. In this chapter, we
develop such a computational approach for modeling the mechanical response of a
representative volume of concrete in uniaxial cyclic loading. A mesoscale is
defined such that it represents an equivalent heterogeneous medium: nonlinear
local response is modeled in the framework of Thermodynamics with Internal
Variables; spatial variability of the local response is represented by
correlated random vector fields generated with the Spectral Representation
Method. Macroscale response is recovered through standard ho-mogenization
procedure from Micromechanics and shows salient features of the uniaxial cyclic
response of concrete that are not explicitly modeled at mesoscale.
