A diffusive dynamic brittle fracture model for heterogeneous solids and porous materials with implementation using a user-element subroutine

This paper addresses brittle fracture simulation using the phase-field modelling (PFM) as an effective and prominent method to predict crack onset and topology in heterogeneous solids and porous materials. This includes the study of the significant crack behaviour change due to the inhomogeneous nature of the materials, where the Weibull distribution is used for creating spatial variations of the material properties. The permanent changes in the permeability and volume fractions of the individual constituents in the cracked porous domain are appropriately accounted for. The present work combines the well-established macroscopic Theory of Porous Media (TPM) and the PFM by means of a user element (UEL) in the software ABAQUS. The coupled system of TPM and PFM equations is then solved in a monolithic fashion for both homogeneous and heterogeneous cases. Numerical examples present a comparative study demonstrating the difference in fracture patterns between homogeneous and heterogeneous solids and porous cases.