Ductile honeycombs under in-plane biaxial loads fail by elastic buckling, plastic yielding and fast fracture of solid cell edges, while brittle honeycombs fail by elastic buckling, brittle rupturing and fast fracture of solid cell edges. In the paper, we aim at summarizing the modeling and theoretical expressions for describing the failure surfaces of honeycombs with non-uniform thickness cell edges under in-plane biaxial loads. Hence, the failure surfaces of ductile honeycombs with plateau borders are generated and found to be dependent on the solid distribution in cell edges and the yielding strengths of solid cell edges. Also, the failure surfaces of brittle honeycombs with plateau borders are significantly affected by the cell-edge modulus of rupture and the solid distribution in cell edges.
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