Lattice Element Model Elastic Behaviour in Solid Mechanics: Bayesian-Based Calibration and Fine-Tuning

This work investigates the elastic behaviour of a mechanical discrete lattice element model based on Timoshenko beam elements. Due to the selected irregular meshes generated with Delaunay triangulation and one-dimensional elements, lattice models struggle to correctly simulate a wide range of elastic material responses, particularly in capturing lateral deformations associated with variations in the material’s Poisson ratio. To address this limitation, we introduce correction coefficients that modify the stiffness properties of the lattice beam elements, influencing the global mechanical behaviour of the lattice. A Bayesian stochastic identification framework is chosen to calibrate these coefficients using a set of standard mechanical tests, ensuring consistency with the proper continuum elastic response. The applicability of the identified lattice element stiffnesses is evaluated across different loading conditions and material properties. The methodology ensures a fine tuning of the model, accuracy in simulating mechanical deformations, and the basis for non-linear phenomena, crack initiation and its propagation across the lattice.