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Abstract Cellular materials have drawn increasing interest in numerous applications due to their promising specific stiffness, strength and energy absorption capacity. In this work, a variety of rather novel lattice topologies pertinent to additive manufacturing are derived and examined. A number of these are derived by free-domain and constrained domain topology optimization procedures, while others are inspired by the triply periodic minimum surface (TPMS) sheet-based topologies. The topology optimization module utilized a single objective function of minimizing strain energy under linear elastic conditions. A total of fifteen different lattice topologies are investigated numerically, including both novel and conventional topologies (e.g. strut-based lattices) and their effective elastic properties are determined with respect to relative density through finite element analysis (FEA). Based on the preliminary FEA results, a number of these topologies are selected of which tessellated lattice structures are fabricated through laser powder bed fusion (LPBF) additive manufacturing technique out of Nylon thermoplastic material. The tessellated lattice structures are experimentally tested in compression and their mechanical performance, including uniaxial modulus, yield strength, and energy absorption capacity (EAC), is assessed. FEA simulations have been conducted using an elastic-plastic constitutive model for the Nylon base material. Both the experimental and numerical results reveal that the mechanical performance of the novel tube-based TPMS lattice P-100 and the combined loading (CL) topology derived through free-domain topology optimization surpasses all other topologies. P-100 uses a primitive TPMS with equal-length tubular connections in each direction, where the tubular length percentage compared to the primitive lattice size is 100%, while CL lattice topology is a free domain topology optimized under compressive loads on the centers of faces, edges, and vertices toward the center. The innovative lattice topologies proposed in the current study, particularly the P-100 and CL topologies, can become crucial in applications where it is necessary to improve the energy absorption capacity, such as sandwich panel cores, supports, and infills for 3D printed components. [ABSTRACT FROM AUTHOR]

[Display omitted] • Pyramidal lattice structures (PLS) with I-shaped struts were 3D printed via DLP. • The utilization of I-shaped struts led to an increase in energy absorption of up to 68%. • Lateral buckling of the lattice struts was observed in the tailored PLS. • The measurements and observed collapse modes were in good agreement with FE predictions. • Specific cross-sectional designs can achieve enhancements in strength of up to 93%. This study examines the compressive response of geometrically tailored pyramidal lattice structures composed of struts with I-shaped cross-sections. Geometrically tailored pyramidal lattices with micro-scale features are 3D printed using the Digital Light Processing (DLP) technique, and their effective elastic modulus, collapse strength and energy absorption capacity are experimentally evaluated under quasi-static compressive loading. Furthermore, detailed non-linear finite element (FE) calculations are performed to examine underlying collapse mechanisms and explore the vast design space offered by the proposed geometrical tailoring scheme. Both the experimental and numerical results show that the geometrically tailored lattice structures outperform conventional pyramidal lattices of equal weight in terms of elastic modulus (+24 %), collapse strength (+21 %) and energy absorption (+68 %). Notably, these strength improvements are attributed to lateral buckling that prompts the I-shaped struts to bend sideways during collapse. Specific cross-sectional designs demonstrate remarkable enhancements in strength and energy absorption, reaching up to 93 % and 161 %, respectively, differentiating them significantly from conventional designs. [ABSTRACT FROM AUTHOR]

• 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]

Metamaterials are architected cellular materials, also known as lattice materials, that are inspired by nature or human engineering intuition, and provide multifunctional attributes that cannot be achieved by conventional polymeric materials and composites. There has been an increasing interest in the design, fabrication, and testing of polymeric metamaterials due to the recent advances in digital design methods, additive manufacturing techniques, and machine learning algorithms. To this end, the present review assembles a collection of recent research on the design, fabrication and testing of polymeric metamaterials, and it can act as a reference for future engineering applications as it categorizes the mechanical properties of existing polymeric metamaterials from literature. The research within this study reveals there is a need to develop more expedient and straightforward methods for designing metamaterials, similar to the implicitly created TPMS lattices. Additionally, more research on polymeric metamaterials under more complex loading scenarios is required to better understand their behavior. Using the right machine learning algorithms in the additive manufacturing process of metamaterials can alleviate many of the current difficulties, enabling more precise and effective production with product quality. [ABSTRACT FROM AUTHOR]