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Continuous fiber fused filament fabrication (CF4) is a layer-by-layer additive manufacturing technique that deposits continuous fiber fused filaments (CFFFs) with a significant in-plane variation of the fiber trajectory, thereby offering great flexibility in fabricating variable-stiffness composite laminates (VSCLs). We introduce a topology optimization method for the design of additively manufactured VSCLs made of overlapping, fiber-reinforced bars. The proposed method is based on geometry projection (GP) techniques, whereby the bars are represented by high-level geometric primitives. As in other GP techniques, this high-level parameterization is mapped onto a fixed structured finite element mesh for conducting analysis, as in densitybased topology optimization techniques. However, unlike previous GP techniques that have demonstrated their applicability in designing structures as assemblies of individual fiberreinforced components, this work focuses on the design of composite structures that adhere to CF4 manufacturing processes. Therefore, we first formulate a material interpolation scheme that better captures the stiffness at the composite’s joints obtained from bar overlaps as a stack. Second, the proposed material interpolation employs composite laminate theory to capture the in-plane and out-of-plane behavior of the structure. Third, to produce designs that conform to the CF4 process, we also proposed a novel length constraint formulation in the form of penalization on the projection scheme, which ensures a minimum length for all the bars. This minimum length limit does not require adding a constraint to the optimization problem. The efficacy and efficiency of the proposed method are demonstrated by a series of compliance minimization problems with in-plane and/or out-of-plane loading. The methodology is also applied to the design of a displacement inverter compliant mechanism. 

Abstract This broad review summarizes recent advances and “hot” research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25–27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a “snapshot” of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions.