Comparative numerical and experimental study of homogenized and full-scale fe models for sandwich structures with re-entrant and anti-tetrachiral auxetic cores

Abstract

Additive manufacturing (AM), widely known as 3D printing, has transformed the field of structural design by enabling the fabrication of complex, lightweight, and highly customized architectures that are often impossible to produce using conventional manufacturing techniques. This technological advancement has unlocked new possibilities for the exploration of architected materials, particularly auxetic structures, which exhibit a negative Poisson's ratio. Auxetic materials, when stretched, expand laterally rather than contracting, and when compressed, they contract inwards rather than bulging. This counterintuitive behavior imparts auxetic structures with remarkable mechanical advantages, including superior energy absorption, enhanced impact resistance, and improved damping performance, making them highly attractive for a wide range of engineering applications. In particular, re-entrant and anti-tetrachiral lattice geometries have emerged as promising auxetic designs due to their tunable mechanical responses, near-isotropic behavior under specific loading conditions, and ability to withstand large deformations while maintaining stability. These features make them well-suited for use in aerospace panels, biomedical implants, and protective systems such as armor panels for defense applications. Despite the advantages of auxetic designs, their complex lattice architectures, composed of intricate geometrical features and periodic unit cells, present significant challenges in numerical modeling and simulation. Full-scale finite element analysis (FEA), which resolves each geometric detail, provides detailed insight into localized stress distributions, deformation patterns, and failure mechanisms. However, this approach demands substantial computational resources, with the complexity of mesh generation, solver runtimes, and post-processing increasing rapidly as the size of the model grows. For large-scale engineering systems like heat exchangers or energy-absorbing panels, where millions of unit cells may be present, full-scale FEA becomes impractical within typical design workflows. To address these challenges, homogenization techniques have been developed as an alternative strategy. By approximating the periodic lattice as an equivalent orthotropic or anisotropic continuum, homogenization enables significant reductions in model complexity, allowing engineers to analyze large and complex structures more efficiently. Nevertheless, homogenization may struggle to capture localized stress concentrations and detailed deformation behaviors, highlighting the trade-off between accuracy and computational efficiency. This study undertook a comprehensive investigation of sandwich structures incorporating re-entrant and anti-tetrachiral auxetic cores, comparing the mechanical behavior of full-scale and homogenized finite element models under different loading conditions. The research also benchmarks these numerical models against experimental tests to provide a robust assessment of their performance. The study begins with the 3D modeling of the two auxetic lattice designs, using Siemens NX 12 software to generate detailed CAD models of both re-entrant and anti-tetrachiral geometries. These designs were selected based on their prevalence in the literature and their contrasting structural characteristics. The full-scale models capture every geometric feature of the lattice, while the homogenized models simplify the complex geometry into an equivalent orthotropic continuum, derived through numerical homogenization techniques. The physical specimens were fabricated using a Stratasys Objet Connex 1 3D printer via the material jetting method, with VeroBlue RDG840 polymer chosen as the base material due to its suitable mechanical properties and compatibility with high-precision additive manufacturing. To determine the fundamental material properties of VeroBlue RDG840, tensile tests were conducted on printed tensile specimens, establishing key parameters such as Young's modulus, Shear Modulus, Poisson's ratio, and density for use in the numerical simulations. In addition, compression tests were performed to determine the corresponding Young's modulus under compressive loading. Following fabrication, the experimental phase involved a series of mechanical tests to evaluate the structural response of the lattice specimens. Modal response testing was performed using the roving hammer technique to identify the natural frequencies and mode shapes, providing insights into the dynamic behavior of the structures. Static compression tests were conducted on cube-shaped specimens to assess their load-bearing capacity and stress-strain behavior under uniaxial compression. Three-point bending tests were also performed to evaluate the flexural stiffness and deformation response of the sandwich panels under bending loads. These experimental results provided essential benchmarks for comparing the numerical models and evaluating the applicability of the homogenization approach. In the numerical phase, finite element models were developed in ANSYS Workbench 2020 R2 for both full-scale and homogenized representations of the re-entrant and anti-tetrachiral structures. The Material Designer module in ANSYS was used to derive the equivalent orthotropic material properties for the homogenized models, based on representative unit cell analyses. Sensitivity studies were conducted to evaluate the effects of mesh density, unit cell selection, and boundary conditions on the accuracy of the homogenized properties. These homogenized models were then used in modal, compression, three-point bending, and tensile FE analyses to assess the global mechanical behavior of the structures under different loading scenarios. The results indicate that modal analyses yielded the closest and most promising match between numerical predictions and experimental benchmarks, demonstrating a strong positive outcome for the homogenization approach in capturing dynamic behavior, such as natural frequencies and mode shapes. This highlights modal analysis as the most suitable scenario for applying homogenized finite element models in auxetic structures, offering both accuracy and significant computational savings. The compression analyses also showed highly promising results, with homogenized models closely matching full-scale simulations and experimental test data, particularly in predicting global stiffness and load-displacement behavior. In contrast, the three-point bending analyses revealed the largest discrepancies, indicating that homogenized models have limitations in accurately representing detailed local deformation patterns, stress concentrations, and complex failure mechanisms under bending loads. While minor differences were also observed in detailed deformation patterns under tensile loading, these differences were generally within acceptable ranges for engineering applications focusing on global response. Additionally, the study demonstrated that the accuracy of three-point bending simulations strongly depends on the correct definition of material behavior under both tensile and compressive loading. The incorporation of averaged and separately defined Young's modulus for tension and compression significantly improved the correlation between numerical and experimental results. This highlights the necessity of accurate material calibration in modeling polymer-based auxetic lattices to achieve physically consistent predictions of bending and flexural responses. Overall, these findings confirm that while homogenized models are highly effective for early-stage design, parametric evaluations, and large-scale system analyses, full-scale finite element models remain essential for accurately capturing local stress distributions, failure initiation, and nonlinear deformations in complex auxetic sandwich structures. This thesis provides a systematic comparison of full-scale and homogenized finite element models for sandwich structures with re-entrant and anti-tetrachiral auxetic cores, highlighting the trade-offs between computational efficiency and accuracy. Homogenization significantly reduces model complexity and solution times while maintaining sufficient accuracy for global analyses, though careful benchmarking against experimental results is essential. The study emphasizes the importance of considering manufacturing imperfections, such as anisotropy and dimensional variability, in modeling strategies. It offers practical insights for engineering applications where homogenized models enable efficient analysis of large-scale systems. Finally, the findings provide a foundation for future work in hybrid modeling strategies that combine homogenized global models with localized full-scale analyses for enhanced design precision.