Mean-Field Homogenization of Time-Evolving Microstructures with Viscoelastic Phases: Application to a Simplified Micromechanical Model of Hydrating Cement Paste

Abstract

Homogenization of random media is a widely used practical and efficient tool to estimate the effective mechanical behavior of composite materials. However, when the microstructure evolves with respect to time, due to phase transformations, care should be taken when upscaling behaviors that themselves involve time, such as viscoelasticity. A natural assumption is to consider that the influence of microstructure evolution is negligible once the material is macroscopically loaded: it allows one to take advantage of the correspondence principle when the phases are nonaging linear viscoelastic. A new approach is proposed to overcome this limitation, building an equivalent composite replacing transforming phases by fictitious aging viscoelastic phases. This equivalent composite has a constant microstructure but is made up of aging linear viscoelastic phases. Its effective behavior can then be estimated taking advantage of recent approaches to homogenize such behaviors. Applications to cement paste are proposed, referring to a simplified morphological model. In particular, the approximation introduced when neglecting microstructure evolution is investigated. Qualitatively, compliance functions from evolving microstructure are found to be closer to the experimental ones.