A multi-scale approach of Mode I Crack in ettringite

Ettringite, as one of the hydration products of cement paste, has attracted the attention of pavement engineers recently. In this paper, a concise and comprehensive multi-scale modelling approach is presented to study the Mode I fracture based on the continuum level tool Phase-field Theory (PFT) and the atomistic level tool Molecular Dynamics (MD) Simulation. The PFT is a new modelling and computational tool used to predict the crack propagation using a phase-field variable, which assumes to be positive one in the intact solid and negative one in the crack region. Realising the fact that at the crack tip, the PFT is unable to deal with the singularity of stress and strain, and thus we use the MD Simulation to further investigate mechanical performances at a finer level. By the energy coupling the two different approaches at the crack tip, we present the two-way multi-scale coupling simulation of ettringite to simulate Mode I cracking fracture. The comparison between our multi-scale results with results from the traditional fracture mechanics proves that our multi-scale model is reasonable.