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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]

Owing to the advancements in additive manufacturing and increased applications of additively manufactured structures, it is essential to fully understand both the elastic and plastic behavior of cellular materials, which include the mathematically-driven sheet lattices based on triply periodic minimal surface (TPMS) that have received significant attention recently. The compressive elastic and plastic behaviors have been well established for many TPMS latticed structures, but not under multiaxial loading. Furthermore, TPMS lattices are computationally expensive to model explicitly when used in latticing various structures for enhanced multi-functionality, and hence the need to develop accurate yield surfaces in order to capture their plastic behavior in a homogenized approach. The majority of previous yield surfaces developed for cellular materials originate from cellular foams, and limited attempts has been made to develop yield surfaces for TPMS lattices. In this study, a numerical modeling framework is proposed for developing the initial yield surface for cellular materials and is used to develop the initial yield surface for Schoen's IWP sheet-based TPMS cellular lattices. The effect of different loading conditions on the effective yield strength of the IWP sheet-based (IWP-s) TPMS lattice is numerically investigated, based on a single unit cell of IWP-s under fully periodic boundary conditions, assuming an elastic-perfectly plastic behavior of the base material, for relative densities (ρ ‾) ranging from 7% to 28%. In order to account for different loading conditions, the stress state is characterized in a generalized fashion through the Lode parameter (L). The effect of L is studied over a range of mean stress values (σ m) to understand the effect of both L and σ m on the effective yield strength. An initial yield surface is developed incorporating the effect of L , σ m and ρ ‾ , and is validated numerically showing rather good agreement. In the 3D principal stress space, the shape of the yield surface for the IWP-s lattice resembles the shape of a cocoa pod. [Display omitted] • Extensive numerical finite element simulations on Schoen's IWP triply periodic minimal surface. • An initial yield surface is established and proposed for cellular materials, accounting the third deviatoric stress invariant J 3 , through the incorporation of Lode parameter L. • The initial yield surface is validated at three different loading cases, and is compared to other three well established yield surface for cellular materials. • Proposed yield surface has predicts the initial yielding of IWP-TPMS markedly well. [ABSTRACT FROM AUTHOR]