Numerical homogenization of a linearly elastic honeycomb lattice structure and comparison with analytical and experimental results
Article [Accepted Manuscript]
Is part of
Mechanics of materials ; vol. 167.Publisher(s)
ElsevierAffiliation
- Université de Montréal. Faculté de médecine. École de kinésiologie et des sciences de l'activité physique
- École polytechnique (Montréal, Québec). Laboratoire de mécanique multi-échelles (LM2)
- Université de Montréal. Laboratoire de simulation et modélisation du mouvement
- Hôpital Sainte-Justine. Centre de recherche
Abstract(s)
This paper presents a verification and validation analysis of Finite Element
(FE) models predicting the mechanical response of linearly elastic honeycomb
structures. We have studied three main models, namely: analytical models
based on beam theories, explicit FE models where the cell geometry is explicitly meshed with 3D elements, and numerical homogenized FE models where
a plate made of a honeycomb structure is meshed with 2D elements whose
mechanical properties were predicted from numerical homogenization. We
compared the predictions of these simulations against experimental uni-axial
tensile tests where we mechanically tested 3D printed honeycomb specimens
having a relative density of 40% and made of 13 and 37 cells, respectively.
Comparison of the experimentally measured axial stiffness to the numerical
predictions revealed that the numerical homogenization models can predict
the apparent in-plane stiffness in structures made of 37 cells within 4%, while
the discrepancy increases to 70% when 13 cells are considered. To quantify
this discrepancy, we also provided a relationship between the number of represented cells and the discrepancy of the numerical homogenized model against
the explicit FE models to predict the in-plane stiffness. We believe that these
results could be important for the application of the homogenized models in
optimization of honeycomb lattice structures whose relative density varies with
space.