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Investigation of Titanium Lattice Structures for Biomedical Implants
Published in Ashwani Kumar, Mangey Ram, Yogesh Kumar Singla, Advanced Materials for Biomechanical Applications, 2022
Vijay Kumar Meena, Prashant Kumar, Tarun Panchal, Parveen Kalra, Ravindra Kumar Sinha
Two significant lattice structures with “infinitely periodic surfaces and a mean curvature of zero” have been discovered by Schwarz and Schoen [45,46]. Triply periodic minimal surface (TPMS) Diamond and TPMS Gyroid are the names given to these lattice structures. TPMS structures, unlike manually formed structures, are constructed mathematically utilizing a variety of algorithms and have no need for any post-processing to enhance or integrate the structures [47,48]. “Triply periodic” means that the structure can be packed together in a periodic 3D pattern and “minimal surface” means that it locally minimizes the surface area for a given boundary such that the mean surface curvature at each point is zero. The lack of points of curvature-discontinuity ensured by these architectures is expected to reduce the stress concentration and ultimately to enhance the fatigue strength [49].
Fused Filament Fabrication of cellular, lattice and porous mechanical metamaterials: a review
Published in Virtual and Physical Prototyping, 2023
Enrique Cuan-Urquizo, Rafael Guerra Silva
Triply Periodic Minimal Surface structures. Different triply periodic minimal surfaces (TPMS) have also been fabricated via FFF. These structures can be found as surface-based and strut-based (known in the literature as skeletal (Kladovasilakis et al. 2021)). Among the structures that have been reported, the ones that are more frequently encountered are the so-called schwarzites (named after Hermann Schwarz (Mackay and Terrones 1991; Terrones and Mackay 1992)), specifically: Schwarz-primitive (Figure 6a), gyroid (Figure 6b), and Schwarz-diamond (Figure 6c) (Gaal et al. 2021; Felix et al. 2020; Kladovasilakis, Tsongas, and Tzetzis 2021; Sajadi et al. 2018; Mishra, Chavan, and Kumar 2021; Maconachie et al. 2020; Kladovasilakis et al. 2021; de Aquino, Maskery, and Longhitano 2020; Alizadeh-Osgouei et al. 2021). These geometries can be built from trigonometric expressions, as reported in (Kladovasilakis, Tsongas, and Tzetzis 2021).
Comparative analysis of mechanical properties and energy absorption capabilities of functionally graded and non-graded thermoplastic sheet gyroid structures
Published in Mechanics of Advanced Materials and Structures, 2022
Ramon Miralbes, Saul Higuera, David Ranz, Jose Antonio Gomez
Advances in additive manufacturing (AM) could solve some of these problems because new geometries can be developed with different optimized energy-absorbing structures and configurations depending on the part of the head to be protected. In this way, triply periodic minimal-surface (TPMS) structures are identified to be extremely efficient solutions [6, 7], because they exhibit a minimal area in three coordinate directions, zero mean curvature free of straight lines and intersections, and low anisotropy [8]. Furthermore, strut-based structures have some angle limitations [9], require additional supports in the manufacturing process [10], and present stress concentration near the joint; TPMSs do not have these angle limitations or need these supports [11, 12] and exhibit a more uniform stress distribution [9, 13–15]. Note that TPMSs also present higher fatigue endurance [16, 17].
Design of graded lattice structures in turbine blades using topology optimization
Published in International Journal of Computer Integrated Manufacturing, 2021
Ebrahim Ahmed Ali Alkebsi, Hacene Ameddah, Toufik Outtas, Abdallah Almutawakel
Lattice structures attract a considerable attention in a number of fields including: aerospace and biomedical industry. The need for lattice structures comes from their contribution in weight reduction and easing the control of the mechanical and physical properties of the component (Tang, Kurtz, and Zhao 2015; Cutolo et al. 2020). In addition, lattice structures can absorb energy, control the heat transfer easily as it has an effective surface area, and allow freedom in designing without the need for wholly change the structural shape (i.e replacing the solid part of the component with lattice structures in the required areas) (Du et al. 2020; Nishizu et al. 2017). This is what leads to think of using lattice structures in the manufacture of the turbine blades. In this work, authors replace the internal solid part of the blade with graded lattice structures taking into account achieving appropriate homogenization between the material, unit cell and AM technique to reach the best mechanical and physical properties for these lattice structures (Duan et al. 2020). Understanding the topological relationship between lattices and its component materials is a key factor in allowing blades to be designed with improved end-use characteristics (Abou-AAbou-Ali et al. 2019). However, the main challenge remains in choosing the suitable lattice design. The authors suggest three different lattice structures with implicit surfaces derived from the triply periodic minimal surface (TPMS) namely: Diamond, Gyroid and Primitive. Due to their appealing topological characteristics, TPMS structures depend on mathematical formulas to create surfaces and connect them with high efficiency to produce a three-dimensional structure through curved surfaces and multiple voids (Al-Ketan, Al-Rub, and Rowshan 2017). TPMS lattices are mathematically defined using level-set approximation equations (Abou-AAbou-Ali et al. 2019; Tripathi and Shukla 2017). The software MATLAB is used to model these equations consisting of trigonometric functions. Table 3 presents the unit cell of each TPMS. For each unit cell of TPMS obtained, the authors use the lattice structure topology optimization (LSTO) in ANSYS based on the homogenization method to form the graded lattice structure built from these cells which were replicated in 3D with optimal distribution to fulfil a given load case(Zhang, Yang, and Kun 2018; Maskery et al. 2018). In the other hand, the manufacturability of complex TPMS lattices depends highly on Additive Manufacturing technology because of its engineering flexibility and high ability to exploit and compile the complex results of optimizing topology.