Three-dimensional lattice model for coupling of fracture and mass transport

Dual lattices are combined to model the coupling of fracture and mass transport in quasi-brittle materials. Elemental connectivity within the mechanical lattice, representing elasticity and fracture, is defined by the Delaunay tessellation of a random set of points. The connectivity of conduit elements within the transport lattice is defined by the Voronoi tessellation of the same set of points. The enforcement of boundary conditions is facilitated by a novel procedure for discretising the domain boundaries. The use of dual lattices provides a natural means for simulating transport along cracks and from the crack surfaces into the bulk material. The properties of conduit elements evolve with the crack opening values of neighbouring mechanical elements. Through benchmark comparisons involving non-stationary flow and fracture, the proposed dual lattice approach is shown to be objective with respect to element size and orientation.