A stochastic multi-scale approach for numerical modeling of complex materials - Application to uniaxial cyclic response of concrete

Abstract

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 ismodeled 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 RepresentationMethod. Macroscale response is recovered through standard homogenization procedure fromMicromechanics and shows salient features of the uniaxial cyclic response of concrete that are not explicitly modeled at mesoscale.