High-entropy alloys are solid solutions of multiple principal elements that are capable of reaching composition and property regimes inaccessible for dilute materials. Discovering those with valuable properties, however, too often relies on serendipity, because thermodynamic alloy design rules alone often fail in high-dimensional composition spaces. We propose an active learning strategy to accelerate the design of high-entropy Invar alloys in a practically infinite compositional space based on very sparse data. Our approach works as a closed-loop, integrating machine learning with density-functional theory, thermodynamic calculations, and experiments. After processing and characterizing 17 new alloys out of millions of possible compositions, we identified two high-entropy Invar alloys with extremely low thermal expansion coefficients around 2 × 10 ⁻⁶ per degree kelvin at 300 kelvin. We believe this to be a suitable pathway for the fast and automated discovery of high-entropy alloys with optimal thermal, magnetic, and electrical properties.

Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grübler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

Flat-foldable origami tessellations are periodic geometric designs that can be transformed from an initial configuration into a flat-folded state. There is growing interest in such tessellations, as they have inspired many innovations in various fields of science and engineering, including deployable structures, biomedical devices, robotics, and mechanical metamaterials. Although a range of origami design methods have been developed to generate such fold patterns, some non-trivial periodic variations involve geometric design challenges, the analytical solutions to which are too difficult. To enhance the design methods of such cases, this study first adopts a geometric-graph-theoretic representation of origami tessellations, where the flat-foldability constraints for the boundary vertices are considered. Subsequently, an optimization framework is proposed for developing flat-foldable origami patterns with four-fold (i.e., degree-4) vertices, where the boundaries of the unit fragment are given in advance. A metaheuristic using particle swarm optimization (PSO) is adopted for finding optimal solutions. Several origami patterns are studied to verify the feasibility and effectiveness of the proposed design method. It will be shown that in comparison with the analytical approach and genetic algorithms (GAs), the presented method can find both trivial and non-trivial flat-foldable solutions with considerably less effort and computational cost. Non-trivial flat-foldable patterns show different and interesting folding behaviors and enrich origami design.