Concentration and homogenization in evolving, complex, and multiphase microstructures : theory and application to NMR- and humidity-monitored cementitious materials

Many heterogeneous materials have microstructures which are hierarchically organized across several orders of magnitude. It is of fundamental scientific interest in engineering mechanics to establish quantitative links between microstructural properties and the macroscopic behavior of such materials. This is setting the scene for the theoretical part of the presentthesis. It is methodically rooted in continuum micromechanics and focused on innovative approaches to the "stress average rule" and "strain concentration tensors". The latter renderscale transitions possible, e.g. they enable (i) downscaling of the macrostrains imposed on representative volume elements of micro heterogeneous materials to the strains experiencedby the microstructural constituents, as well as (ii) upscaling of the elastic stiffness and the eigenstress of the microstructural constituents to their macroscopic counterparts.Cementitious materials are particularly challenging when it comes to multiscale modeling. They exhibit evolving microstructures at early material ages, because of the chemical reaction between the water and the binder. The finally formed microstructures consist of solid constituents and pores with characteristic sizes ranging across four orders of magnitude: from a few tens of micrometers to a few single nanometers. Many macroscopic properties of cementitious materials result from physico-chemical processes occurring at nanometric scales. This is setting the scene for the application part of the present thesis. It is focused on two challenging topics regarding multiscale modeling of cement pastes: the evolution of the volume fractions of the microstructural constituents at early material ages and sorption-induced macroscopic volume changes at mature material ages. The present thesis strives for establishing a synthesis between fundamental developments and challenging applications in the field of multiscale mechanics. (author)