PSI - Issue 28

Florian Vlădulescu et al. / Procedia Structural Integrity 28 (2020) 637–647 Vl ă dulescu and Constantinescu / Structural Integrity Procedia 00 (2019) 000–000

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their high stiffness to weight ratio and tunable properties, lattice structures, alternatively known as cellular structures, have been extensively connected to metal additive manufacturing by Rosen (2007) and Murr et al. (2010), and gradually applied to various fields, such as aerospace such as aerospace (Shapiro et al. 2016) and biomechanical (Murr et al. 2010; Arabnejad et al. 2016). The development of 3D printing technologies made nowadays possible to produce such metallic and non-metallic materials. Classically, lattice structures can be divided to be periodic or stochastic from their layout patterns. Extensive studies have been carried out to demonstrate the superior performance of periodic lattices compared to stochastic ones. In a review on design and structural optimization in AM done by Plocher et al. (2019) it was emphasized that expertise-driven structural optimization such as latticing is not always having lightweight as an objective, as stiffness is greatly compromised in exchange for e.g. aesthetics or multiphysics requirements, but rather constitutes a design practice. Topology optimization (TO), a well-known structural design method, was focused by Sigmund (2001) on the homogenization approach and the implementation of density based TO put the foundation for the nowadays methods. The most prominent TO approaches can be summarized as follows: density-based; level set; evolutionary/genetic algorithms; topological derivatives and phase field (Huang and Xie 2010, Sigmund and Maute 2013). Multiscale optimization considers that design optimization is applied at two scales: the macroscale, where the structure is optimized, and the microscale, where the material is optimized (Sivapuram 2016) . Thus, structure and material are optimized simultaneously. The multiscale design optimization was done by linearizing and formulating a new way to decompose into macro and microscale design problems in such a way that solving the decomposed problems separately lead to an overall optimum solution. The hierarchical solution strategy proposed by Rodrigues et al. (2002) allows a unique microstructure to be optimized for each macroscale finite element. Homogenization is used to obtain effective material properties of the microstructures, which are then used to determine the macroscale structural performance. The hierarchical method is similar to the homogenization approach to topology optimization developed by Bendsøe and Kikuchi (1988) who employed the size and rotation of square or rectangular microscale voids within each macroscale element as the design variables. The difference being that Rodrigues et al. 10 utilizes the complete topological freedom that is available for optimization at microscale. Although the hierarchical scheme optimizes the topology at two scales, design variables only exist at the microscale. However, the mechanical behavior of lattice structures could be quite different when their feature sizes are comparable to the length scale of the global structure, referred to as mesostructures. In this instance, lattices can no longer be taken as micro architectured materials but are designed as primary load bearing parts. AM makes possible the fabrication of multiscale cellular structures as a whole part, for which features can span several dimensional scales. Both the configurations and layout pattern of the cellular lattices have great impact on the overall performance of the lattice structure. As mentioned by Cheng et al. (2018), TO is still not sufficiently developed to design AM components. The work payed special attention to lattice structure topology optimization (LSTO) for AM and addressed a novel aspect in the concurrent optimization of lattice infill and design-dependent movable features, on which boundary conditions were prescribed. Variable density lattices (Lynch et al. 2018) can be tailored according to structural and functional requirements. That is, lattice ligaments may be thicker where a load path requires significant structural support but thinner where less loading is transmitted. Additionally, lattice density can be locally tailored to accommodate natural frequency, pressure drop and/or heat dissipated into a cooling fluid, or other design objectives. The goal of multi-scale optimization method that can generate conformal gradient lattice structures (CGLS) is to achieve gradient density, adaptive orientation, and variable scale (or periodic) lattice structures with the highest mechanical stiffness (Li et al. 2020). A new lattice optimization methodology developed by Daynes et al. (2019) tailors the size, shape, and orientation of individual lattice trusses in three-dimensional space by using principal strain fields obtained from topology optimization. This new method of generating functionally graded lattices is shown both numerically and experimentally to be capable of generating lattice structures with greatly improved stiffness and strength when compared to lattice structures with a uniform lattice infill. Another approach is to design lattice structures that conform with both the principal stress directions and the boundary of the optimized shape (Wu et al. 2019). Their method consists of two major steps: the first optimizes concurrently the shape (including its topology) and generates the distribution of orthotropic lattice materials inside the shape as to maximize stiffness under the application of specific external loads; the second takes the optimized configuration (i.e. locally-defined orientation, porosity, and anisotropy) of lattice materials from the previous step, and extracts a globally consistent lattice structure by field-aligned parameterization. The anisotropy resulting from AM can become a benefit if printing is done, with