Mathematics of concrete: Case Studies in non-periodic averaging - Adrian Muntean

Abstract

In this talk, my attention will focus on a simple reaction-diffusion scenario (sulphuric acid attack) taking place in an unsaturated chemically-active material (concrete). Deviating from the standard assumption on the uniform periodicity of the distribution of microstructures (here: pores), I consider locally-periodic arrays of pores and then scale up the PDE model to an observable level, where non-distructive macroscopic measurements can be done. The working technique I choose to use provides not only effective coefficients and fluxes, but also ensures corrector estimates on both concentrations and transport fluxes -- quantitative measures of the error produced by the averaging procedure.