Definition and implementation of a robust homogenized constitutive law for aluminum honeycomb crushing

Aluminum honeycombs are bio-inspired structures widely used in the aeronautical, automotive, and space industries due to their high specific strength and excellent energy absorption capabilities. These features make them ideal for crashworthiness applications. However, their energy absorption strongly depends on the loading orientation, which complicates the definition of a homogenized constitutive law capable of accurately capturing their crushing behavior. Such homogenized laws are essential to reduce computational costs in large-scale simulations. Existing models in literature often rely on constitutive laws with uncoupled degrees of freedom, which may lead to material instability under complex loading conditions. This work presents the development and implementation of a robust homogenized constitutive law for aluminum honeycomb crushing. An initial material database was generated through a campaign of static and dynamic numerical tests, and the resulting mechanical properties were fitted to the honeycomb's geometrical parameters. A code was developed to define the orthotropic elastic tensor based on these properties, including automated stability checks and corrections when necessary. Subsequently, an orthotropic plastic potential was calibrated. After demonstrating the limitations of Hill's potential due to its purely deviatoric nature, a non-associated Deshpande–Fleck plasticity model was adopted and validated through convexity checks and appropriate adjustments. The resulting implementation proved to be robust and reliable. The homogenization procedure was verified and validated against highly localized impact scenarios, showing errors below 10%. Finally, a bottoming law was calibrated using a Monte Carlo approach, further improving accuracy. The novelty of this work lies in the combination of automated stability enforcement, 3D non-associated plasticity based on Hill's and Deshpande-Fleck potentials, fully implementable homogenization framework for honeycomb crushing. Compared to detailed finite element models, the proposed homogenized law achieved an average reduction of approximately 85% in computational time.