Additive manufacturing (AM) and topology optimization strongly complement each other in that the complex and optimal designs created through the latter can directly be fabricated through AM, leading to reduced design and fabrication time.

As AM expands into multi-material fabrication, there is a natural need for efficient multi-material topology optimization methods, where one must simultaneously optimize the topology, and the distribution of various materials within the topology.

In this paper we generalize the single-material Pareto tracing method of topology optimization to multiple materials, and discuss its implementation using assembly-free finite element analysis, and first-order element-sensitivity. The effectiveness of the algorithm is demonstrated through illustrative examples.

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