Strong 3D Printing by TPMS Injection

Explicit Topology Optimization of Voronoi Foams

Topology optimization can maximally leverage the high DOFs and mechanical potentiality of porous foams but faces challenges in adapting to free-form outer shapes, maintaining full connectivity between adjacent foam cells, and achieving high simulation accuracy. Utilizing the concept of Voronoi tessellation may help overcome the challenges owing to its distinguished properties on highly flexible topology, natural edge connectivity, and easy shape conforming. However, a variational optimization of the so-called Voronoi foams has not yet been fully explored. In addressing the issue, a concept of explicit topology optimization of open-cell Voronoi foams is proposed that can efficiently and reliably guide the foam's topology and geometry variations under critical physical and geometric requirements. Taking the site (or seed) positions and beam radii as the DOFs, we explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a highly efficient local finite difference method to estimate the derivatives. During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The foam's mechanical property is also computed with a much-improved efficiency by an order of magnitude, in comparison with benchmark FEM, via a new material-aware numerical coarsening method on its highly heterogeneous density field counterpart. We show the improved performance of our Voronoi foam in comparison with classical topology optimization approaches and demonstrate its advantages in various settings.

Topology Optimization Via Spatially-Varying TPMS

Structural design with multi-family triply periodic minimal surfaces (TPMS) is a meaningful work that can combine the advantages of different types of TPMS. However, very few methods consider the influence of the blending of different TPMS on structural performance, and the manufacturability of final structure. Therefore, this work proposes a method to design manufacturable microstructures with topology optimization (TO) based on spatially-varying TPMS. In our method, different types of TPMS are simultaneously considered in the optimization to maximize the performance of designed microstructure. The geometric and mechanical properties of the unit cells generated with TPMS, that is minimal surface lattice cell (MSLC), are analyzed to obtain the performance of different types of TPMS. In the designed microstructure, MSLCs of different types are smoothly blended with an interpolation method. To analyze the influence of deformed MSLCs on the performance of the final structure, the blending blocks are introduced to describe the connection cases between different types of MSLCs. The mechanical properties of deformed MSLCs are analyzed and applied in TO process to reduce the influence of deformed MSLCs on the performance of final structure. The infill resolution of MSLC within a given design domain is determined according to the minimal printable wall thickness of MSLC and structural stiffness. Both numerical and physical experimental results demonstrate the effectiveness of the proposed method.

Analysis of mechanical characteristics and permeability of TPMS and Voronoi porous structure for bone scaffold

Bionic porous structure has been widely used in the field of bone implantation, because it can imitate the topological structure of bone, reduce the elastic modulus of metal bone implantation, and meet the mechanical properties and material transmission characteristics after implantation. This paper mainly studies the effects of different bionic porous structures on the mechanical and material transport properties of bone scaffolds. Firstly, under the same porosity condition, 12 groups of bionic porous structures with different shapes were designed, including G, P, D, I-type three period minimal surface (TPMS) and Voronoi porous structures with different irregularities. Then uses ABAQUS to carry out mechanical finite element simulation on different bionic porous structures, and uses Ti-6Al-4V alloy as forming material, uses laser powder bed fusion technology (LPBF) to prepare the scaffold, then carries out compression experiments. At the same time, COMSOL software is used to simulate the flow characteristics, analyze the permeability characteristics, and verified through cell experiment in vivo. The results show that the mechanical and permeability are different with vary scaffolds. In terms of topology, the morphological characteristics of TPMS are similar to trabecular bone, its compressive strength is relatively strong. Voronoi scaffold has lower elastic modulus, which can provide sufficient mechanical support while reducing stress shielding. In addition, the permeability of TPMS scaffold is better than Voronoi scaffold, which is helpful to promote cell proliferation and bone ingrowth. These bionic porous structures have their own advantages. Therefore, when designing porous structures for bone implantation, it is necessary to select the appropriate porous structure according to different bone implantation requirements. The research will help promote the clinical application of porous structures in the field of bone implantation, and provide theoretical support for the exploration of bone implantation structure design.

Evaluation of Compressive and Permeability Behaviors of Trabecular-Like Porous Structure with Mixed Porosity Based on Mechanical Topology

The mechanical properties and permeability properties of artificial bone implants have high-level requirements. A method for the design of trabecular-like porous structure (TLPS) with mixed porosity is proposed based on the study of the mechanical and permeability characteristics of natural bone. With this technique, the morphology and density of internal porous structures can be adjusted, depending on the implantation requirements, to meet the mechanical and permeability requirements of natural bone. The design parameters mainly include the seed points, topology optimization coefficient, load value, irregularity, and scaling factor. Characteristic parameters primarily include porosity and pore size distribution. Statistical methods are used to analyze the relationship between design parameters and characteristic parameters for precise TLPS design and thereby provide a theoretical basis and guidance. TLPS scaffolds were prepared by selective laser melting technology. First, TLPS under different design parameters were analyzed using the finite element method and permeability simulation. The results were then verified by quasistatic compression and cell experiments. The scaling factor and topology optimization coefficient were found to largely affect the mechanical and permeability properties of the TLPS. The corresponding compressive strength reached 270-580 MPa; the elastic modulus ranged between 6.43 and 9.716 GPa, and permeability was 0.6 × 10^-9-21 × 10^-9; these results were better than the mechanical properties and permeability of natural bone. Thus, TLPS can effectively improve the success rate of bone implantation, which provides an effective theory and application basis for bone implantation.

Efficient Representation and Optimization for TPMS-Based Porous Structures

In this approach, we present an efficient topology and geometry optimization of triply periodic minimal surfaces (TPMS) based porous shell structures, which can be represented, analyzed, optimized and stored directly using functions. The proposed framework is directly executed on functions instead of remeshing (tetrahedral/hexahedral), and this framework substantially improves the controllability and efficiency. Specifically, a valid TPMS-based porous shell structure is first constructed by function expressions. The porous shell permits continuous and smooth changes of geometry (shell thickness) and topology (porous period). The porous structures also inherit several of the advantageous properties of TPMS, such as smoothness, full connectivity (no closed hollows), and high controllability. Then, the problem of filling an object's interior region with porous shell can be formulated into a constraint optimization problem with two control parameter functions. Finally, an efficient topology and geometry optimization scheme is presented to obtain optimized scale-varying porous shell structures. In contrast to traditional heuristic methods for TPMS, our work directly optimize both the topology and geometry of TPMS-based structures. Various experiments have shown that our proposed porous structures have obvious advantages in terms of efficiency and effectiveness.