Strength and other mechanical properties of cement and concrete rely upon the formation of calcium-silicate-hydrates (C-S-H) during cement hydration. Controlling structure and properties of the C-S-H phase is a challenge, due to the complexity of this hydration product and of the mechanisms that drive its precipitation from the ionic solution upon dissolution of cement grains in water.Departing from traditional models mostly focused on length scales above the micrometer, recent research addressed the molecular structure of C-S-H. However, small-angle neutron scattering, electron-microscopy imaging, and nanoindentation experiments suggest that its mesoscale organization, extending over hundreds of nanometers, may be more important. Here we unveil the C-S-H mesoscale texture, a crucial step to connect the fundamental scales to the macroscale of engineering properties. We use simulations that combine information of the nanoscale building units of C-S-H and their effective interactions, obtained from atomistic simulations and experiments, into a statistical physics framework for aggregating nanoparticles. We compute small-angle scattering intensities, pore size distributions, specific surface area, local densities, indentation modulus, and hardness of the material, providing quantitative understanding of different experimental investigations. Our results provide insight into how the heterogeneities developed during the early stages of hydration persist in the structure of C-S-H and impact the mechanical performance of the hardened cement paste. Unraveling such links in cement hydrates can be groundbreaking and controlling them can be the key to smarter mix designs of cementitious materials.U pon dissolution of cement powder in water, calcium-silicate-hydrates (C-S-H) precipitate and assemble into a cohesive gel that fills the pore space in the cement paste over hundreds of nanometers and binds the different components of concrete together (1). The mechanics and microstructure are key to concrete performance and durability, but the level of understanding needed to design new, more performant cements and have an impact on the CO 2 footprint of the material is far from being reached (2).Most of the experimental characterization and models used to predict and design cement performance have been developed at a macroscopic level and hardly include any material heterogeneity over length scales smaller than micrometers (3). However, EM imaging, nanoindentation tests, X-rays and neutron scattering, and NMR analysis as well as atomistic simulations have now elucidated several structural and mechanical features concentrated within a few nanometers (4-8). The hygrothermal behavior of cement suggests a hierarchical and complex pore structure that develops during hydration and continues to evolve (1, 9-11). NMR and small-angle neutron scattering (SANS) studies of hardened C-S-H identified distinctive features of the complex pore network and detected significant structural heterogeneities spanning length scales between tens and hu...

Cement is the most widely used manufacturing material in the world and improving its toughness would allow for the design of slender infrastructure, requiring less material. To this end, we investigate by means of molecular dynamics simulations the fracture of calcium-silicate-hydrate (C-S-H), the binding phase of cement, responsible for its mechanical properties. For the first time, we report values of the fracture toughness, critical energy release rate, and surface energy of C-S-H grains. This allows us to discuss the brittleness of the material at the atomic scale. We show that, at this scale, C-S-H breaks in a ductile way, which prevents from using methods based on linear elastic fracture mechanics. Knowledge of the fracture properties of C-S-H at the nanoscale opens the way for an upscaling approach to the design of tougher cement.

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The simplest form of a sufficiently realistic description of the fracture of concrete as well as some other quasibrittle materials is a bilinear softening stress-separation law (or an analogous bilinear law for a crack band). This law is characterized by four independent material parameters: the tensile strength, f t , the stress σ k at the change of slope, and two independent fracture energies-the initial one, G f and the total one, G F . Recently it was shown that all of these four parameters can be unambiguously identified neither from the standard size effects tests, nor from the tests of complete load-deflection curve of specimens of one size. A combination of both types of test is required, and is here shown to be sufficient to identify all the four parameters. This is made possible by the recent data from a comprehensive test program including tests of both types made with one and the same concrete. These data include Types 1 and 2 size effects of a rather broad size range (1:12.5), with notch depths varying from 0 to 30 % of cross section depth. Thanks to using identically cured specimens cast from one batch of one con-C. G. Hoover Northwestern University, Evanston, IL, USA Present address: C. G. Hoover M.I.T., Cambridge, MA, USA Z. P. Bažant (B) Northwestern University, 2145 Sheridan Road, CEE/A135, Evanston, IL 60208, USA e-mail: z-bazant@northwestern.edu crete, these tests have minimum scatter. While the size effect and notch length effect were examined in a separate study, this paper deals with inverse finite element analysis of these comprehensive test data. Using the crack band approach, it is demonstrated: (1) that the bilinear cohesive crack model can provide an excellent fit of these comprehensive data through their entire range, (2) that the G f value obtained agrees with that obtained by fitting the size effect law to the data for any relative notch depth deeper than 15 % of the cross section (as required by RILEM 1990 Recommendation), (3) that the G F value agrees with that obtained by the work-of-fracture method (based on RILEM 1985 Recommendation), and (4) that the data through their entire range cannot be fitted with linear or exponential softening laws.

The application of machine learning to predict materials’ properties usually requires a large number of consistent data for training. However, experimental datasets of high quality are not always available or self-consistent. Here, as an alternative route, we combine machine learning with high-throughput molecular dynamics simulations to predict the Young’s modulus of silicate glasses. We demonstrate that this combined approach offers good and reliable predictions over the entire compositional domain. By comparing the performances of select machine learning algorithms, we discuss the nature of the balance between accuracy, simplicity, and interpretability in machine learning.

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The universal size-shape effect law is a law that describes the dependence of nominal strength of specimen or structure on both its size and the crack (or notch) length, over the entire range of interest, and exhibits the correct small-size and large-size asymptotic properties as required by the cohesive crack model (or crack band model). The main difficulty has been the transition of crack length from 0, in which case the size effect is Type 1, to deep cracks (or notches), in which case the size effect is Type 2 and is fundamentally different from Type 1, with different asymptotes. In this transition, the problem is not linearizable because the notch is not much larger than the fracture process zone. The previously proposed universal law could not be verified experimentally for the Type 1-Type 2 transition because sufficient test data were lacking. The current study is based on recently obtained comprehensive fracture test data for three-point bend beams cast from one batch of the same concrete and cured and tested under identical conditions. The test data reveal that the Type 1-Type 2 transition in the previous universal law has insufficient accuracy and cannot be captured by Taylor series expansion of the energy release rate function of linear elastic fracture mechanics. Instead, the size effect for a zero notch and for the transitional range is now characterized in terms of the strain gradient at the specimen surface, which is the main variable determining the degree of stress redistribution by the boundary layer of cracking. The new universal law is shown to fit the comprehensive data quite well, with a coefficient of variation of only 2.3%.

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