Voronoi-cell lattice modeling of the elastic behavior of pultruded glass fiber reinforced polymers

The rapidly increasing use of pultruded glass fiber reinforced polymer (GFRP) elements in structural engineering applications brings opportunities and challenges for novel modeling strategies to simulate the mechanical behavior of this class of materials with higher accuracy and computational efficiency. In this context, this work introduces a new methodology using the Voronoi-cell Lattice Model (VCLM), a form of random lattice modeling, to simulate the elastic behavior of orthotropic GFRP structural elements, directly accounting for any admissible combination of fiber-to-matrix stiffness ratio and fiber orientation. First, the manuscript introduces the analytical derivations required to evaluate the elastic properties to assign to the lattice elements as a function of the geometrical relationships between the material planes of symmetry and the element orientation. The model is verified against analytical solution of canonical deformation problems, and further validated by means of experimental data previously obtained by the co-authors. Moreover, the numerical predictions are also compared to established theories such as the Tsai-Hill and Kim’s criteria. Following validation, a sensitivity analysis is carried out to investigate the influence of different fiber-to-matrix and Young’s modulus ratios on the macroscopic response of the structures. Results demonstrate that both mechanical parameters significantly influence the macroscopic elastic response (i.e., macroscopic stiffness and Poisson’s ratio) when employing a discrete lattice network discretization. These findings provide a new understanding of the capabilities and challenges associated with the adoption of random lattice modeling approaches for the simulation of non-isotropic media, with particular attention devoted to establishing formal relationships between the lattice-level mechanical parameters and the resulting macroscopic response of the structures.