Discrete element modeling on nanoindentation creep behavior of C-S-H under berkovich and flat-tip indenters

Abstract

This paper employs the discrete element method (DEM) to simulate the nanoindentation creep of calcium-silicate-hydrate (C-S-H), focusing on indentation deformation, particle interactions, and stress transmission paths. The Rate Process Theory (RPT), previously utilized in the creep modeling of cohesive soils and other granular materials, is proposed to simulate C-S-H creep. Due to the nanometer size of C-S-H particles, the critical time step in DEM simulations is very small. Therefore, a time-scaling algorithm is used to match the DEM simulation time with the physical time in laboratory tests, accelerating the simulation time by a factor of 1 × 10⁸. C-S-H particle assemblies with specific packing densities are generated using Particle Flow Code (PFC3D, version 5.0), with coordination numbers and cohesion forces controlled by the stress-servo of PFC walls. Virtual nanoindentations using a Berkovich indenter are conducted on C-S-H particle assemblies with three different packing densities (0.74, 0.64, and 0.58), followed by parameters calibration. Results show that the DEM + RPT method can capture the scaling relations between the indentation modulus, hardness, and contact creep modulus of C-S-H particle assemblies and the packing density. Furthermore, DEM simulations reveal particle rearrangement under Berkovich and flat-tip indenters, highlighting that different indenter types lead to distinct creep kinetics in C-S-H, with the Berkovich indenters experimentally capturing long-term creep and flat-tip indenters measuring short-term creep.