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Abstract This review highlights recent progress in additive manufacturing (AM) techniques for polymer composites reinforced with nanoparticles, short fibers, and continuous fibers. It also explores the integration of functional resins and fibers to enable advanced capabilities such as shape morphing, enhanced electrical and thermal conductivity, and self-healing behavior. Building on these advances, the review examines computational design strategies that optimize material distribution and fiber orientation. Representative approaches range from density-based methods to emerging level-set topology optimization frameworks, with objectives evolving from improving mechanical performance to addressing complex multi-physics functional requirements. The review also identifies emerging opportunities, including the need for technological innovations to further improve mechanical properties and enable adaptable multifunctionality. Further advances in theoretical modeling and integrated design-printing workflows are also discussed. By synthesizing these developments, this review aims to foster interdisciplinary collaborations and accelerate innovation in AM-enabled composite materials across a wide range of applications. 

Abstract Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted meshes, immersed boundary methods instead embed the computational domain in a structured background grid. Interpolation-based immersed boundary methods augment existing finite element software to non-invasively implement immersed boundary capabilities through extraction. Extraction interpolates the structured background basis as a linear combination of Lagrange polynomials defined on a foreground mesh, creating an interpolated basis that can be easily integrated by existing methods. This work extends the interpolation-based immersed isogeometric method to multi-material and multi-physics problems. Beginning from level-set descriptions of domain geometries, Heaviside enrichment is implemented to accommodate discontinuities in state variable fields across material interfaces. Adaptive refinement with truncated hierarchically refined B-splines (THB-splines) is used to both improve interface geometry representations and to resolve large solution gradients near interfaces. Multi-physics problems typically involve coupled fields where each field has unique discretization requirements. This work presents a novel discretization method for coupled problems through the application of extraction, using a single foreground mesh for all fields. Numerical examples illustrate optimal convergence rates for this method in both 2D and 3D, for partial differential equations representing heat conduction, linear elasticity, and a coupled thermo-mechanical problem. The utility of this method is demonstrated through image-based analysis of a composite sample, where in addition to circumventing typical meshing difficulties, this method reduces the required degrees of freedom when compared to classical boundary-fitted finite element methods.