A phase-field approach to fracture coupled with diffusion

A phase-field model is proposed to describe cracking and its coupling with diffusion. While our specific interest is on diffusion of chloride ions in hardened cement paste, the proposed model has more general applicability to any porous material potentially developing cracks. The model is formulated in Gurtin's framework and first applied to a two-dimensional plate subject to mechanical and diffusion boundary conditions, where an analytical solution can be found. Several more complex examples solved with the finite element method demonstrate the ability of the model to capture the effect of cracking on the local and on the macroscopically measured diffusivities. Experimental results from the literature are used to calibrate the relationship between local diffusivity and phase-field parameter. The calibrated relationship is applied to a unit cell problem, which serves as the first step towards the coupled diffusion-mechanical analysis at the mesoscale of concrete.