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In this paper, a two-step homogenization method is proposed and implemented for evaluating effective mechanical properties of lattice structured material fabricated by the material extrusion additive manufacturing process. In order to consider the characteristics of the additive manufacturing process in estimation procedures, the levels of scale for homogenization are divided into three stages — the levels of layer deposition, structural element, and lattice structure. The method consists of two transformations among stages. In the first step, the transformation between layer deposition and structural element levels is proposed to find the geometrical and material effective properties of structural elements in the lattice structure. In the second step, the method to estimate effective mechanical properties of lattice material is presented, which uses a unit cell and is based on the discretized homogenization method for periodic structure. The method is implemented for cubic lattice structure and compared to experimental results for validation purposes.

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Truss-like cellular structures have great potential to be applied in light-weight design applications. However, determining the appropriate designs for these truss-like cellular structures can be a challenging task due to their geometric complexities and prohibitive computational costs in the design process. In this research, a new design method is proposed which can drastically reduce computational costs and design parameters, while maintaining the performance of the targeted outcome. Furthermore, the proposed method facilitates cellular structure designs that can handle multiple loading conditions. The proposed method utilizes the relative density information obtained from a solid topology optimization to automatically determine the diameter of each individual strut in the structure, which collectively represent the set of design variables. This allows the method to produce lattice structures that can perform reliably under multiple loading conditions and also reduce the computational cost associated with the design of these structures. The efficacy of the developed method is compared to existing methods including the size matching and scaling method that combines solid-body analysis and a predefined unit-cell library.