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In nature, structural and functional materials often form programmed three-dimensional (3D) assembly to perform daily functions, inspiring researchers to engineer multifunctional 3D structures. Despite much progress, a general method to fabricate and assemble a broad range of materials into functional 3D objects remains limited. Herein, to bridge the gap, we demonstrate a freeform multimaterial assembly process (FMAP) by integrating 3D printing (fused filament fabrication (FFF), direct ink writing (DIW)) with freeform laser induction (FLI). 3D printing performs the 3D structural material assembly, while FLI fabricates the functional materials in predesigned 3D space by synergistic, programmed control. This paper showcases the versatility of FMAP in spatially fabricating various types of functional materials (metals, semiconductors) within 3D structures for applications in crossbar circuits for LED display, a strain sensor for multifunctional springs and haptic manipulators, a UV sensor, a 3D electromagnet as a magnetic encoder, capacitive sensors for human machine interface, and an integrated microfluidic reactor with a built-in Joule heater for nanomaterial synthesis. This success underscores the potential of FMAP to redefine 3D printing and FLI for programmed multimaterial assembly. 

Frieze groups are discrete subgroups of the full group of isometries of a flat strip. We investigate here the dynamics of specific architected materials generated by acting with a frieze group on a collection of self-coupling seed resonators. We demonstrate that, under unrestricted reconfigurations of the internal structures of the seed resonators, the dynamical matrices of the materials generate the full self-adjoint sector of the stabilized group C*-algebra of the frieze group. As a consequence, in applications where the positions, orientations and internal structures of the seed resonators are adiabatically modified, the spectral bands of the dynamical matrices carry a complete set of topological invariants that are fully accounted by the K-theory of the mentioned algebra. By resolving the generators of the K-theory, we produce the model dynamical matrices that carry the elementary topological charges, which we implement with systems of plate resonators to showcase several applications in spectral engineering. The paper is written in an expository style. 

Elastic surface waves pumping is realized by a smart pillar-type metasurface.