Developing scaling laws to predict compressive mechanical properties and determine geometrical parameters of modified BCC lattice structures

The objective of this study is to develop generalized empirical closed-form equations to predict the compressive mechanical properties and determine geometrical parameters. To achieve that, 117 models are built and analyzed using ABAQUS/CAE 2016 to provide two types of reliable data: one for lattice mechanical properties based on finite element method and the other for geometrical parameters using the measurements of ABAQUS diagnostic tool. All the models are created by modifying the basic feature of body-centered cubic lattice structure based on a range of strut angles, a set of relative densities, and two design sets. Also, the influence of lattice cell tessellations and material distribution at strut intersections are considered within these models to provide accurate results. The first data set is fitted with the scaling laws, relating relative elastic modulus and stress with the relative density, to determine Gibson and Ashby's coefficients. The second type of data regarding lattice geometries is correlated with the relative density to estimate actual lattice volume, strut radius, aspect ratio, and overall lattice volume. By this way, these equations can be used to predict directly the lattice characteristics and geometrical parameters without the need for ABAQUS. The results show that the generalized empirical closed-form equations can predict well both the lattice characteristics and geometries. In addition, the relative stresses and elastic modulus increase with increasing the strut angles since the main deformation mechanisms move toward stretch-dominated rather than bending. Besides, Gibson and Ashby's coefficients along with the geometrical factors of aspect ratios are found to be approximately similar for both generations. This study contributes to developing efficient equations to provide the researchers with a preliminary insight about the best lattice design and its compatibility in a certain application before starting the fabrication process.