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• An initial yield surface is established and proposed for cellular materials. • Five loading cases are considered to evaluate the performance of the yield surface. • Five sheet-based triply periodic minimal surface lattices are investigated. • The proposed yield criterion shows accurate yielding predictions for all cases. Triply periodic minimal surfaces (TPMS), which are a class of architected cellular materials, have attracted significant attention lately, due to their prevailing mechanical, electrical and chemical properties, to name a few, and due to the advancements in additive manufacturing technologies that make it possible to print such materials. However, simulating the elastic-plastic mechanical behavior of structural systems (e.g., beams, plates, cores of sandwich panels, structural systems with various levels of geometric complexity) that are latticed with thousands of TPMS lattices are computationally expensive to model explicitly, and hence the need to develop accurate yield surfaces in order to capture their plastic behavior in a homogenized approach. In this work, a generalized initial yield criterion is proposed for sheet-based TPMS lattices, which incorporates the Lode parameter L. The initial yielding of five different sheet-based TPMS lattices are investigated in five different loading conditions. These lattices are Schoen's I-WP (IWP-s), Gyroid (GYR-s), Diamond (DIA-s), F-RD (FRD-s) and Primitive (PRIM-s). The proposed yield criterion accurately predicts the initial yielding of all these lattices in all the loading conditions considered, outperforming other yield criteria currently proposed in literature. [Display omitted] [ABSTRACT FROM AUTHOR]