A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials - Application to Uniaxial Cyclic Response of Concrete

TL;DR

This paper introduces a stochastic multi-scale computational approach to model the complex, uncertain, and nonlinear mechanical response of concrete under uniaxial cyclic loading, integrating mesoscale heterogeneity and macroscale behavior.

Contribution

It develops a novel multi-scale stochastic modeling framework combining Thermodynamics with Internal Variables and spectral random fields for concrete response simulation.

Findings

Successfully captures key features of cyclic response

Integrates multi-scale heterogeneity and uncertainty

Provides a comprehensive modeling approach for complex materials

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 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.