A nanoscale numerical model of calcium silicate hydrate P.C. Fonseca a,⇑ , H.M. Jennings b , J.E. Andrade c a Drexel University, Department of Civil, Architectural and Environmental Engineering, Philadelphia, PA, United States b Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, Cambridge, MA, United States c California Institute of Technology, Department of Civil Engineering and Applied Mechanics, Pasadena, CA, United States article info Article history: Received 21 December 2009 Received in revised form 25 April 2011 Available online 31 May 2011 Keywords: DEM Nanoindentation Microstructure C–S–H abstract This manuscript presents a numerical model of the low-density and high-density calcium– silicate–hydrate (C–S–H) gel phases in cement paste. Generated using an autocatalytic growth algorithm, C–S–H is introduced as an assemblage of discrete granular particles at nanoscale with realistic particle-level properties, such as elastic modulus, friction, and cohesion. Using the discrete element method, nanoindentation simulations are performed on each phase, demonstrating that its mechanical contact properties compare well to the results from nanoindentation experiments in the literature. By creating an additional loosely packed phase of C–S–H and maintaining constant particle-level material properties, the results further show that the indentation modulus, as a function of the volumetric packing fraction of the C–S–H gel phase, compares well to a linear self-consistent scaling relation while the hardness most closely fits a nonlinear self-consistent scaling relation. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Calcium silicate hydrate (C–S–H) 1 is the primary binding phase in cement-based materials and is the constituent responsible for macroscale cohesion and durability of con- crete structures. C–S–H has been described as a gel consist- ing of separate nanoscale particles with mechanical properties dominated by surface forces (Wittmann, 1976). However, the relationship between this nanostructure and the properties of structural concrete are not fully under- stood. Models are becoming increasingly important to pre- dict the bulk properties of cement and concrete, such as shrinkage, creep, permeability, and cracking. C–S–H is responsible for much of the cohesive proper- ties in concrete but the chemical origin of this cohesion is uncertain. Models by Nonat, Jönsson, Pellenq, and col- leagues suggest cohesion stems primarily from electro- static surface charge and, to a lesser extent, from van der Waals forces and capillary tension (Pellenq and Damme, 2004; Jönsson et al., 2004; Nonat, 2004). Although they do not necessarily believe that C–S–H manifests as distinct colloids, their ideas on cohesion are not incompatible with a particulate model. Attractive forces measured by atomic force microscopy (AFM) measure 1 nN forces between sur- faces (Lesko et al., 2001, 2004). Drawing on information from previous models (Jen- nings and Tennis, 1994) and experimental evidence (Allen et al., 1987), the proposed numerical model for C–S–H is composed of discrete particles each 5 nm in diameter. These particles form two distinct packing densities, known as high-density (HD) and low-density (LD) C–S–H (Jen- nings, 2000; Tennis and Jennings, 2000; Jennings, 2007). This information makes it possible to analyze C–S–H at a bulk scale using only particle-level information as input. From the following proposed model of C–S–H, indentation properties of the primary binding phase of cement paste will be determined and compared to experimental values in the literature. Using the discrete element method (DEM), nanoindentation simulations on each phase of C– S–H will be performed. By quantitatively comparing these 0167-6636/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmat.2011.05.004 ⇑ Corresponding author. Tel:. +1 215 571 3786. E-mail addresses: fonseca@drexel.edu, illa@u.northwestern.edu (P.C. Fonseca), hmj@mit.edu (H.M. Jennings), jandrade@caltech.edu (J.E. An- drade). 1 Cement chemistry notation: C = CaO, S = SiO 2 ,H=H 2 O. Mechanics of Materials 43 (2011) 408–419 Contents lists available at ScienceDirect Mechanics of Materials journal homepage: www.elsevier.com/locate/mechmat