Fig. 5: Mechanical properties of C-A-S-H at varying Ca/Si and Al/Si ratios.

a Bulk modulus approximated by the Hill scheme. b Young’s modulus approximated by the Hill scheme. c Shear modulus approximated by the Hill scheme. d–f Comparisons of the Young’s modulus projections on the XY, XZ, and YZ planes for different Ca/Si ratios (with Al/Si = 0.10). g–i Comparisons of the Young’s modulus projections on the XY, XZ, and YZ planes for different Al/Si ratios (with Ca/Si = 1.7). j, k Linear regression relationship between the elastic tensor components C11, C22, and Mean chain length (MCL). l Relationship between C33 and the linear density of interlayer Ca. The first number in the subscript of the elastic constants represents the direction of the applied force, while the second number indicates the material’s response in the corresponding direction. The red line is derived from the linear fitting. ‘*’ refers to the presence of interlayer Al(V) in the C-A-S-H structure. The square, diamond, triangle, and circle represent Ca/Si ratios of 1.3, 1.5, 1.7, and 1.9, respectively.