Cellular metamaterials are of immense interest for many current engineering applications. Tailoring the structural organization of cellular structures leads to new metamaterials with superior properties leading to low weight and very strong/stiff materials. Incorporation of hierarchy to regular cellular structures enhances the properties and introduces novel tailorable metamaterials.

For many complex cellular metamaterials, the only realistic manufacturing process is additive manufacturing (AM). The use of AM to manufacture large structures may lead to several types of defects during the manufacturing process, such as missing/broken cell walls, irregular thickness, flawed joints, missing (partial) layers, and irregular elastic plastic behavior due to toolpath. For large structures, it would be beneficial to understand the effect of defects on the overall performance of the structure to determine if the manufacturing defect(s) are significant enough to abort and restart or whether the material can still be used.

Honeycomb structures are used for the high strength to weight ratio applications. These metamaterials have been studied and several models have been developed based on idealized cell structures to explain their elastic plastic behavior. However, these models do not capture real-world manufacturing defects resulting from AM. The variation of elastic plastic behavior of regular honeycomb structures with defects has been studied, but the performance of hierarchical honeycomb structures with defects is still unknown. In this study, the effects of missing cell walls are investigated to understand the elastic behavior of hierarchical honeycomb structures through simulations using finite element analysis. Regular (zero order), first order and second order hierarchical honeycombs have been investigated in this study. The first level of hierarchy has been implemented by changing each three edge vertex of a regular hexagonal honeycomb lattice by adding another smaller hexagon. The second level of hierarchy is created by adding another smaller hexagon at each three edge vertex of the hexagons added for the first order hierarchy. For the hierarchical cases, the overall density of the honeycomb is held constant to the parent structure (zero order or regular) by reducing the thickness of the cell wall in the first and second order structures. ANSYS® was used to develop finite element models to analyze the performance of both perfect and defected regular, first order and second order hierarchical honeycombs. Defects were added to the model by randomly removing cell walls. Hierarchical honeycombs demonstrated more sensitivity to missing cell walls than regular honeycombs. On average, the elastic modulus decreased by 45% with 5.5% missing cell walls for regular honeycombs, 60% with 4% missing cell walls for first order hierarchical honeycomb and 95% with 4% missing cell walls for second order hierarchical honeycombs.

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