Stochastic lattice modeling of correlated graphene disorder

Nanoscale disorder in graphene is commonly modeled as spatially uncorrelated variability of interatomic parameters, although atomistic fluctuations and microstructural effects often exhibit spatial organization over finite length scales. The influence of such spatial correlation on the apparent mechanical response of graphene remains largely unexplored. This work introduces a novel stochastic lattice mechanics framework in which the correlation length of interatomic variability is treated as an explicit control parameter governing the elastic response of finite graphene sheets. Bond stretching and angular stiffness parameters are modeled as spatially correlated random fields with physically bounded marginal distributions, enabling systematic uncertainty propagation from the lattice scale to apparent elastic properties. Virtual uniaxial tensile tests along the zigzag and armchair directions are performed to evaluate directional Young's moduli and Poisson's ratios. The results show that spatial correlation affects not only the dispersion of elastic properties but also their mean values. Increasing correlation length produces correlation-induced stiffening and amplifies elastic anisotropy by promoting spatially coherent load-bearing regions and reducing microscopic self-averaging. Spatial correlation additionally alters the coupling between axial stiffness and transverse deformation, leading to systematic shifts and increased variability of Poisson's ratios. These findings identify correlation length as a higher-order parameter governing the apparent elastic behavior of graphene and establish spatial organization of nanoscale disorder as a mechanically significant mechanism in two-dimensional lattice materials. The proposed framework provides a computationally efficient tool for stochastic graphene analysis and lattice-based modeling of materials with spatially structured nanoscale disorder.