  This work presents a computational method for the design of architected truss
lattice materials where each strut can be made of one of a set of available
materials. We design the lattices to extremize effective properties. As
customary in topology optimization, we design a periodic unit cell of the
lattice and obtain the effective properties via numerical homogenization. Each
bar is represented as a cylindrical offset surface of a medial axis
parameterized by the positions of the endpoints of the medial axis. These
parameters are smoothly mapped onto a continuous density field for the primal
and sensitivity analysis via the geometry projection method. A size variable
per material is ascribed to each bar and penalized as in density-based topology
optimization to facilitate the entire removal of bars from the design. During
the optimization, we allow bars to be made of a mixture of the available
materials. However, to ensure each bar is either exclusively made of one
material or removed altogether from the optimal design, we impose optimization
constraints that ensure each size variable is 0 or 1, and that at most one
material size variable is 1. The proposed material interpolation scheme readily
accommodates any number of materials. To obtain lattices with desired material
symmetries, we design only a reference region of the unit cell and reflect its
geometry projection with respect to the appropriate planes of symmetry. Also,
to ensure bars remain whole upon reflection inside the unit cell or with
respect to the periodic boundaries, we impose a no-cut constraint on the bars.
We demonstrate the efficacy of our method via numerical examples of bulk and
shear moduli maximization and Poisson's ratio minimization for two- and
three-material lattices with cubic symmetry.
