Determination of a lattice material with near - Isotropic properties using equal diameter struts and its application in topology optimization

Lattice materials are preferred in the design of structural components due to their lightweight nature, durable structure, high energy absorption capacity, thermal insulation, and vibration damping capabilities. To design with lattice materials, the topology optimization method, performed under the assumption of isotropic material, is widely used. Using this topology optimization method, it is suitable to employ lattice cells exhibiting isotropic properties for obtaining a design with lattice materials. However, when all strut elements in existing cubic lattice cells have the same diameter, isotropic properties cannot be achieved. To achieve isotropic properties, the strut diameters in the inner and outer regions of the lattice cells can be differentiated, thereby making the properties of the lattice cell isotropic. Nonetheless, using strut of different diameters complicates the modeling process compared to cells where all struts have the same diameter, as it requires modeling struts of varying diameters. Additionally, the modeling process is further constrained by the manufacturability limits of the upper and lower diameter values, restricting the design space. As a solution to these issues, this thesis proposes a lattice cell that exhibits the closest properties to isotropy while all struts in a cubic lattice cell have the same diameter. To this end, the Young's modulus, shear modulus, and Poisson's ratios of various lattice cell types formed by different arrangements of strut elements in a cubic cell were determined using the homogenization method at different relative densities. Using these values, the anisotropy ratios of the cells were calculated, and the face-centered simple cubic (FCSC) cell was identified as the cell type exhibiting properties closest to isotropy. For the identified FCSC cell, the relationship between relative density and homogenized Young's modulus was modeled using two alternatives for the isotropic property function employed in topology optimization: the Solid Isotropic Material with Penalization (SIMP) and the Rational Approximation of Material Properties (RAMP) functions. It was observed that modeling with RAMP yielded more suitable results compared to the SIMP function. The topology optimization process using the RAMP function identified for the FCSC was applied to various example applications. For these examples, the topology optimization results of the obtained lattice material designs were modeled and analyzed with three-dimensional solid elements, and their effectiveness was demonstrated by comparison with results in the literature. Keywords: Lattice material, Topology optimization, Homogenization, Anisotropy ratio, Additive manufacturing