Simulating fracture in rock using a micropolar peridynamic formulation

Mode I opening and mixed-mode I-II fracture experiments were performed with a homogeneous, fine grained sandstone using the three-point bending test. Specimens were notched at various lengths and positions of the beam edge to produce the desired loading condition. A micropolar peridynamic model was used to simulate the fracture initiation and propagation process. The analytical implicit formulation was derived by defining a specific macroelastic energy density function for micropolar non-local lattices, which depends on three deformation parameters: bond stretch, bond shear deformation accounting for the rotational degrees of freedom, and the particle's relative rotation. The micropolar non-local lattice model is capable of handling a variable Poisson's ratio, and is suitable for modelling the mechanical behavior of Cauchy isotropic solids subjected to non-homogeneous deformation fields and fracture. A preliminary analysis on a smooth boundary specimen was performed in order to validate the results obtained with the conceived peridynamic model adopting irregular discretizations. The failure process in notched sandstone specimens was simulated numerically in quasi-static conditions. Numerical results were compared with experimental data obtained from electronic speckle pattern interferometry (ESPI) tests, which were used to quantify and detect the fracture phenomena. Due to the intrinsic features of peridynamic theory, realistic crack patterns and crack initiation angles were obtained from the numerical simulations.