Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, e.g., machining and injection molding or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-tooptimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors' perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.

A monolithic compliant mechanism transmits applied forces from specified input ports to output ports by elastic deformation of its comprising materials, fulfilling required functions analogous to a rigid-body mechanism. In this paper, we propose a level-set method for designing monolithic compliant mechanisms made of multiple materials as an optimization of continuum heterogeneous structures. Central to the method is a multiphase level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure. Combined with the classical shape derivatives, the level-set method yields an Eulerian computational system of geometric partial differential equations, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. The proposed method is demonstrated for single-input and single-output mechanisms and illustrated with several two-dimensional examples of synthesis of multimaterial mechanisms of force inverters and gripping and clamping devices. An analysis on the formation of de facto hinges is presented based on the shape gradient information. A scheme to ensure a well-connected topology of the mechanism during the process of optimization is also presented.

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Metamaterials are defined as a family of rationally designed artificial materials which can provide extraordinary effective properties compared with their nature counterparts. This paper proposes a level set based method for topology optimization of both single and multiple-material Negative Poisson's Ratio (NPR) metamaterials. For multi-material topology optimization, the conventional level set method is advanced with a new approach exploiting the reconciled level set (RLS) method. The proposed method simplifies the multi-material topology optimization by evolving each individual material with a single level set function and reconciling the result level set field with the Merriman-Bence-Osher (MBO) operator. The NPR metamaterial design problem is recast as a variational problem, where the effective elastic properties of the spatially periodic microstructure are formulated as the strain energy functionals under uniform displacement boundary conditions. The adjoint variable method is utilized to derive the shape sensitivities by combining the general linear elastic equation with a weak imposition of Dirichlet boundary conditions. The design velocity field is constructed using the steepest descent method and integrated with the level set method. Both single and multiple-material mechanical metamaterials are achieved in 2D and 3D with different Poisson's ratios and volumes. Benchmark designs are fabricated with multi-material 3D printing at high resolution. The effective auxetic properties of the achieved designs are verified through finite element simulations and characterized using experimental tests as well.

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