A Discrete Element Method–Based Energetic Approach to Model Two‐Dimensional Fatigue Crack Propagation

Abstract

In this work, a fatigue crack propagation model is proposed using the two‐dimensional discrete element method (DEM). The challenge lies in describing the small progressive fatigue crack growth within a single cycle, which is typically much smaller than the size of the smallest particles, making it difficult to continuously capture the loss of contact stiffness. To accurately represent crack increments in DEM, a reduction in contact stiffness is directly linked to the length of the propagated crack, based on the local energy release in a contact. This allows for a precise description of crack increments at scales much smaller than particle size. Building on this, and utilizing the local evaluation of the energy release rate, Paris' law is applied to describe the fatigue behaviour of the contact under cyclic loading. An efficient approach is introduced that replaces the full cycle analysis with equivalent quasi‐static monotonic simulations, leading to significant gains in computational time. The resultant DEM simulations adopt the same parameters as in continuum mechanics, eliminating the need for calibration, and demonstrate good agreement with theoretical and experimental results from the literature.