A peridynamic model for brittle damage and fracture in porous materials

We introduce a peridynamic (PD) model for simulating brittle damage and fracture in elastic porous materials based on an Intermediate Homogenization (IH) approach. In this approach, instead of explicitly representing the detailed pore geometry, we use homogenization but maintain some information about the microstructure (porosity) in the model. Porosity is introduced in the model as initial peridynamic damage, implemented by stochastically pre-breaking peridynamic bonds to match the desired porosity value. We validate the model for elastodynamics using wave propagation speed and apparent elastic moduli in porous glasses of various porosities. We then use the model to study the fracture behavior of Berea sandstone under three-point bending loading conditions and an off-center pre-notch. Results agree very well with experiments: we obtain different failure modes depending on the length of the off-center pre-notch. With a short pre-notch, most damage (and subsequent failure) happens in the center of the beam. In this case, material porosity makes the fracture behavior insensitive to the presence of the off-center pre-notch. With a long pre-notch, damage starts from near its tip, and progresses in mixed mode towards the loading point. The model captures the location of crack initiation to be the right-corner of the notch, exactly as shown by the experimental acoustic emission results. In contrast, a fully-homogenized model for the porous sandstone fails to reproduce the failure mode sensitivity on the prenotch length. The results show the importance of using information from the microscale when trying to capture the important effects local heterogeneities (like pores) have on brittle damage initiation and growth in porous materials.