Multiscale Estimation of Elastic Constants of Hydrated Cement Nilanjan Mitra 1 ; Prodip Sarkar 2 ; Sutapa Deb 3 ; and Subhasish Basu Majumder 4 Abstract: Hydrated cement produces the strength and stiffness of concrete, a widely utilized infrastructural material. Estimation of elastic constants of hydrated cement, a heterogeneous material consisting of numerous constituents, is a complex problem. This paper presents a comprehensive multiscale micromechanical estimation methodology. X-ray diffraction (XRD) investigations along with Rietveld refinements were done to estimate the constituents of hydrated cement. Molecular dynamics investigations were carried out for each individual constituent to determine individual elastic constants. Micro computed tomography (microCT) investigations determined the porosity of the sample at different cross sections and also estimated the pore-size distributions. The Mori–Tanaka homogenization principle was used on the constituent elastic constants to estimate the final elastic constants of the hydrated cement, which were compared with values obtained from experimental investigations in the literature. The methodology demonstrated that consideration of tobermorite (all three phases) and jennite along with the estimated macroporosity can predict the overall stiffness of the cement paste with an error of about 8%. DOI: 10.1061/(ASCE)EM.1943- 7889.0001582. © 2019 American Society of Civil Engineers. Author keywords: Hydration; Rietveld; MicroCT; Molecular dynamics; Mori–Tanaka. Introduction Concrete is one of the most widely used infrastructural materials. The strength and stiffness of concrete is believed to result from the hydration of cement. Hydration of cement has been studied by several researchers; Scrivener et al. (2015) and references therein discussed current advancements on the topic. Constituents of hy- drated cement are the major components behind the formation of mortar for concrete and/or cementitious composites. Hydrated ce- ment components are primarily responsible for strength and stiff- ness development of mortar mix and eventually the strength and stiffness of the mortar, concrete, and/or cementitious mix. An ac- curate macroscopic estimation of the elastic constants should there- fore depend on the individual microscopic constituents of the hydrated cement mix. A comprehensive study was initiated to iden- tify rigorously the different constituents of hydrated cement mix through X-ray diffraction and Rietveld analysis, to determine the elastic constants of each of the components through molecular dy- namic investigations, and then to use homogenization techniques to estimate the macroscopic elastic constants of the hydrated cement mix, which was then assessed by experimental observations at a macroscopic scale. A similar concept of estimation of elasticity of hydrated cement was done through experimental investigations, including nanoin- dentation and homogenization techniques (Constantinides and Ulm 2004). An alternative methodology to that of the nanoindentation technique using molecular dynamic simulations is proposed in this paper. The components in hydrated cement were identified through X-ray diffraction (XRD)/Rietveld analysis, and molecular dynam- ics (MD) investigations determined individual component elastic constants. Based on the estimated porosity from microCT investi- gations, homogenization principles were used to obtain the elastic constants of the hydrated cement. Related studies used MD simulations and homogenization tech- niques to determine the elastic constants of calcium silicate hydrate (CSH) (Al-Ostaz et al. 2010; Zhou et al. 2015; Hajilar and Shafei 2015). The literature argues that CSH is one of the major phases of hydrated cement, and therefore the estimation of CSH provides the properties for hydrated cement paste. However, hydrated cement paste consists of pores/voids as well as many other compounds apart from CSH, and therefore it is necessary to determine the contribution of all possible compounds in the mix to estimate the elastic constants of the mix. As part of this work, detailed XRD/Rietveld analysis was carried out to identify different phases of hydrated cement paste. Although numerous studies reported XRD/Rietveld analyses of hydrated ce- ment, most of these studies did not consider all the components, constituents, and phases that may be present in the mix. Most of the studies, whether they modeled CSH as tobermorite/jennite (T/J) or tobermorite/calcium hydroxide (T/CH) (e.g., Richardson 1999; Richardson 2004), considered only one phase of tobermorite 0.9, 1.1, and 1.4 nm however, a mixture of all these phases may be present in the hydrated cement mix. Variations in the structures of different types of tobermorites 0.9, 1.1, and 1.4 nm are pri- marily caused by the degree of hydration (Merlino et al. 2001). Because the degree of hydration is not homogenous within the hydrated cement mix, there is an obvious possibility that all phases of tobermorite may reside within the hydrated cement 1 Associate Professor, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India (corresponding author). Email: nilanjan@civil.iitkgp.ernet.in 2 Ph.D. Research Scholar, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India. Email: prodipsarkar08@ gmail.com 3 Ph.D. Research Scholar, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India. ORCID: https://orcid .org/0000-0003-4941-0572. Email: sutapadeb@iitkgp.ac.in 4 Professor, Material Science Centre, Indian Institute of Technology Kharagpur, Kharagpur 721302, India. Email: subhasish@matsc.iitkgp .ernet.in Note. This manuscript was submitted on November 14, 2017; approved on September 11, 2018; published online on January 29, 2019. Discussion period open until June 29, 2019; separate discussions must be submitted for individual papers. This paper is part of the Journal of Engineering Mechanics, © ASCE, ISSN 0733-9399. © ASCE 04019014-1 J. Eng. Mech. J. Eng. Mech., 2019, 145(4): 04019014 Downloaded from ascelibrary.org by Indian Institute of Technology Kharagpur on 01/29/19. Copyright ASCE. For personal use only; all rights reserved.