This study explores stress drops and earthquake nucleation within the simplest elasto-plastic media using two-dimensional simulations, emphasizing the critical role of temporal and spatial resolutions in accurately capturing stress evolution and strain fields during seismic cycles. Our analysis reveals that stress drops, triggered by plastic deformation once local stresses reach the yield criteria, reflect fault rupture mechanics, where accumulated strain energy is released suddenly, simulating earthquake behavior. Finer temporal discretization leads to sharper stress drops and lower minimum stress values, while finer spatial grids provide more detailed representations of strain localization and stress redistribution. Our analysis reveals that displacement accumulates gradually during interseismic periods and intensifies during major stress drops, reflecting natural earthquake cycles. Furthermore, the initial wave field patterns during earthquake nucleation are complex, with high-amplitude shear components.</p> <p>The histogram of stress drop amplitudes shows a non-Gaussian distribution, characterized by a sharp peak followed by a gradual decay, where small stress drops are more frequent, but large stress drops still occur with significant probability. This "solid turbulence" behavior suggests that stress is redistributed across scales, with implications for understanding the variability of seismic event magnitudes.</p> <p>Our results demonstrate that high-resolution elasto-plastic models can reproduce key features of earthquake nucleation and stress drop behavior without relying on complex frictional laws or velocity-dependent weakening mechanisms. These findings emphasize the necessity of incorporating plasticity into models of fault slip to better understand the mechanisms governing fault weakening and rupture. Furthermore, our work suggests that extending these models to three-dimensional fault systems and accounting for material heterogeneity and fluid interactions could provide deeper insights into seismic hazard assessment and earthquake mechanics.