Numerical study on the effective stiffness of topology-optimized lattice structures made of orthotropic crystal grains with optimal orientation

Controlling the orientation of crystal grains in metal additive manufacturing is an active field of research. Assuming that three-dimensional control of orthotropic metal crystal grain can be achieved, we numerically studied the effective performance of a topology-optimized lattice made of crystal grains with optimal directions in orientation. The objective function is maximized for an effective isotropic stiffness. The effective properties of the lattice are calculated using the homogenization method. Each discretized finite element is regarded as a crystal grain and its artificial density and orientation are optimized. Through several numerical studies using a single orthotropic crystal of Ni exhibiting large anisotropy in its single crystal stiffness, the optimization and the usefulness of the lattice structure composed of optimal orientation crystal grains is confirmed. In the design of a lattice with effective isotropic stiffness, an improvement in stiffness was observed compared with that using equivalent isotropic Ni as a material.