Self-organized criticality in fracture models at different scales

Although modeling of fractures in solid materials has been within the focus of researchers for decades, a generally applicable and reliable numerical description is still an open topic. The complexity of fracture description hides within its multiscale nature, whereby the nano- and macroscale material behavior often vary significantly, and the transfer between these scales seems to constitute a very challenging task. Thus, in this contribution, we present the possibility of using the framework of self-organized criticality (SOC) as a scale-invariant phenomenon that allows for a physically meaningful connection between the scales. In doing so, we firstly introduce the problem of nanoscale plasticity of amorphous solids using a two-dimensional model network glass. We apply an athermal quasistatic deformation procedure that allows for macroscopic simulation time windows and extracts a power-law distribution regarding the fracture process. Secondly, a macroscale phase-field method (PFM) is applied to simulate fractures in anisotropic viscoelastic materials under quasistatic and dynamic conditions. Together with the fracture width and depth measures during crack propagation, the power-law exponent is discussed to determine whether SOC can be captured using this approach. Numerical examples support the conclusions about the existence/absence of SOC in these models and open the door for a new research topic with PFM for fracture modeling.