PSI - Issue 79

Marco Piacentini et al. / Procedia Structural Integrity 79 (2026) 394–403

397

a

b

Fig. 2. Resulting Voronoi tessellation: (a) generated over the full 3 × 3 periodic tiling; (b) trimmed to the central tile representing the RVE.

= 44 = 2.9 = 77°

= 47 = 2.1 = 22°

= 32 = 1 = 59°

= 16 = 2.3 = 41°

y (mm)

y (mm)

y (mm)

y (mm)

x (mm)

x (mm)

x (mm)

x (mm)

[10, 50],

[1, 3],

[0°, 90°]

Fig. 3. Representative examples of structures with corresponding generation parameters. The range of each parameter is shown at the bottom.

2.2. Finite Element Analysis

FE simulations were performed using the commercial software Abaqus (SIMULIA, Dassault Syste`mes). Python scripting was employed to fully automate the workflow within Abaqus / CAE, including model construction, boundary condition definition, and job submission. Each model corresponded to one of the generated Voronoi-based unit cells described in Section 2.1, where each individual strut was discretized with 4 quadratic Timoshenko beam elements (B22), providing su ffi cient resolution for curvature and local bending e ff ects in the present context. Geometric nonlinearity was enabled to account for large deformations and local buckling. The constituent material (Table 1) was modeled as an isotropic elastic–plastic solid with bilinear hardening, calibrated to reproduce the behavior of Formlabs CLEAR resin as reported by Maurizi et al. (2022a), to enable possible validation with future 3D-printed tests. Periodic boundary conditions (PBCs) were enforced through equation constraints that coupled corresponding nodes on opposite faces of the unit cell, ensuring periodicity of both displacements and rotations. The models were loaded under uniaxial compression, applied by displacement control up to a nominal compressive strain e = − 0 . 2, defined as the ratio of global displacement to the RVE length. Contact interactions were not included, primarily for computational e ffi ciency, as densification phenomena were beyond the present scope of this preliminary study. All analyses were conducted under implicit static equilibrium using the Abaqus / Standard General Static step with automatic increment control. From the results of the simulations, nominal stress σ n was defined as the ratio of the resultant reaction force to the nominal RVE cross-sectional area. The Cauchy stress σ was then obtained, assuming constant volume, as