Chiara Pepi

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 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 used to evaluate the directional Young’s moduli and Poisson’s ratios. The results show that spatial correlation does not only affect the dispersion of elastic properties but also modifies 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. In addition, spatial correlation alters the coupling between axial stiffness and transverse deformation, leading to systematic shifts and increased variability of the Poisson ratios.These findings identify correlation length as a higher-order parameter governing the apparent elastic behavior of two-dimensional lattice materials. The proposed framework provides a computationally efficient tool for stochastic analysis of graphene and more generally for lattice-based modeling of materials with spatially structured nanoscale disorder.

Tie rods play a crucial role in civil engineering, particularly in controlling lateral thrusts in arches and vaults, and enhancing the structural integrity of masonry buildings, both historic and contemporary. Accurately assessing the tensile axial forces in tie rods is challenging due to the limitations of existing methodologies. These methodologies often rely on indirect measurements, computational models, and optimization procedures, resulting in single-point solutions and neglecting both modeling and measurement uncertainties. This study introduces a novel Bayesian updating framework to effectively address these limitations. The framework aims to accurately identify the structural parameters influencing tie rod behavior and estimate uncertainties using natural frequencies as references. A key innovation lies in the mathematical formulation of Bayesian updating, which is founded upon the definition of computational models integrating uncertain updating parameters and latent random variables derived from a rigorous sensitivity analysis aimed at quantifying the impact of the updating parameters on the natural frequencies. Notably, the application of Bayesian updating to the structural identification problem of ancient tie rods represents a significant advancement. The framework provides a comprehensive description of the uncertainties associated with computational models, offering valuable insights for practitioners and researchers alike. Moreover, the results of the sensitivity analysis serve as a valuable tool for setting up inverse problems geared towards accurately identifying tensile axial forces.