PSI - Issue 66

Mansi Gupta et al. / Procedia Structural Integrity 66 (2024) 122–134 Mansi Gupta et al. / Structural Integrity Procedia 00 (2025) 000 – 000

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PBC

Periodic Boundary Conditions

G C K IC

Fracture Energy Fracture Toughness

Molecular dynamics studies on concrete majorly deals with the atomistic simulations of CSH gel. At nanoscale, CSH gel is often described as having a layered structure similar to that of tobermorite minerals, a family of calcium silicate hydrates. These layers consist of silicate chains (SiO₄ tetrahedra) connected by calcium ions. Water molecules and additional calcium ions occupy the interlayer spaces, leading to the formation of a gel-like structure. The silicate chains can be either dimers or longer chains, and the degree of polymerization varies, contributing to the disorder of the structure. Pellenq et al. (2009) put forward a ground breaking work on realistic modelling of CSH gel. Their model accurately predicts the indentation modulus of CSH, with molecular mechanics calculations yielding a modulus of 65 GPa, closely aligning with experimental nano-indentation tests that report a modulus of 56 GPa. Hou et al. (2014) explored the mechanical properties of CSH at the molecular level through uniaxial tension testing in different directions (x, y, z). Their study reveals that the layered structure of CSH results in heterogeneous mechanical properties across different directions. Notably, the z direction, where layers are connected by hydrogen bonds and calcium ions, exhibits the weakest tensile strength. This anisotropy is critical for understanding the linkage between molecular structure and larger-scale mechanical behaviour. Subsequently, Hou et al. (2014) investigated crack formation mechanisms under uniaxial tension using MD simulations, concentrating on CSH gel with voids ranging in size from 0.5 nm to 5 nm. Their research reveals the dual nature of fracture propagation: ductile behaviour is indicated by the strong ionic-covalent connections (Si – O and Ca – O) in the xy plane, which slow down crack coalescence. On the other hand, cracks spread quickly in the interlayer regions in the z direction and are more brittle because to the numerous hydrogen bond breaks. The study emphasises how strain concentration and nanoscale voids affect the formation of cracks. Bauchy et al. (2015) performed molecular dynamics simulations to investigate the fracture toughness of CSH, yielding significant insights into the mechanisms of crack propagation and the influence of microstructure on material fracture resistance. Mohamed et al. (2018) extended the CSH model by Pellenq et al. to develop CSH models with a varied range of Ca/Si ratios using Density Functional Theory (DFT) and classical MD simulations. Liang (2020) used reactive MD simulations to study the mechanical and fracture properties of C-S-H and calcium hydroxide (CH) composites. According to the study, CH composites had the highest Young's modulus and tensile strength, followed by CSH and CSH-CH composites. Fracture toughness is size-independent, as demonstrated by the fracture toughness values for CSH, CH, and their composites that matched experimental findings. Hou et al. (2021) combined the MD modelling with Peridynamics (PD) model allowing for the simulation of fracture processes at a larger scale. Zhang et al. (2021) utilized reactive MD simulations to explore the effects of high temperatures on CSH gels. It was observed that the heat causes partial drying, volumetric shrinkage, disordering, and stiffening of CSH grains, so profoundly changing their mechanical characteristics and atomic scale fracture behaviour. Using reactive MD techniques, Tu et al. (2022) examined at the elastoplasticity of CSH at different strain rates. The findings indicated that the atomistic structure of CSH exhibits mechanical anisotropy, with the y direction demonstrating better mechanical performance and the z direction exhibiting the least mechanical performance. Cao et al. (2024) employed molecular dynamics simulations with the ClayFF force field to investigate the influence of micropore orientation on the fracture behaviour of calcium silicate hydrate (CSH) under tensile stress.The analysis deals with the mechanical properties and energy evolution associated with micro fractures. However, more study is needed in this regard from the perspective of fracture mechanics. The majority of the studies deals with the fracture behaviour of CSH gel under uniaxial tensile loading. However, due to wide application of concrete, the fracture characterisation of CSH under different loadings is also essential. In this study, the mode-I fracture toughness of CSH gel has been studied under three-point bending to simulation the fracture response. 2. Modelling of CSH gel The atomic structure for unit cell of CSH gel is taken from Zhang et al. (2021). The 11 Å tobermorite crystal is taken as a base to develop CSH atomic model as described by Pellenq et al. (2009). The resulting unit cell of CSH