Triclinic Metamaterials by Tristable Origami with Reprogrammable Frustration.

Geometrical-frustration-induced anisotropy and inhomogeneity are explored to achieve unique properties of metamaterials that set them apart from conventional materials. According to Neumann's principle, to achieve anisotropic responses, the material unit cell should possess less symmetry. Based on such guidelines, a triclinic metamaterial system of minimal symmetry is presented, which originates from a Trimorph origami pattern with a simple and insightful geometry: a basic unit cell with four tilted panels and four corresponding creases. The intrinsic geometry of the Trimorph origami, with its changing tilting angles, dictates a folding motion that varies the primitive vectors of the unit cell, couples the shear and normal strains of its extrinsic bulk, and leads to an unusual Poisson effect. Such an effect, associated with reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant mathematical formulae. The nonlinearities of the folding motions allow the unit cell to display three robust stable states, connected through snapping instabilities. When the tristable unit cells are tessellated, phenomena that resemble linear and point defects emerge as a result of geometric frustration. The frustration is reprogrammable into distinct stable and inhomogeneous states by arbitrarily selecting the location of a single or multiple point defects. The Trimorph origami demonstrates the possibility of creating origami metamaterials with symmetries that are hitherto nonexistent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant microrobots.

Micro-structured medium with large isotropic negative thermal expansion.

A challenge in nano- and micro-mechanics is the realization of innovative materials exploiting auxetic behaviour to tailor thermal expansion properties. For this purpose, a new class of micro-structured media possessing an extremely wide range of tunable (positive, negative or even zero) thermal expansion is proposed and analytically and experimentally assessed. For this class of isotropic Mechanical-Auxetic Thermal-Shrinking media, the effective coefficient of thermal expansion is explicitly linked to two microstructural variables via a simple relation, allowing the design with desired values. The theoretical predictions for the negative thermal properties are fully validated by the experimental and numerical outcomes. The simplicity of the proposed structure makes the design useful for the production of a new generation of advanced media, with applications ranging from micromechanical devices to large civil and space structures.

Detecting singular weak-dissipation limit for flutter onset in reversible systems.

A "flutter machine" is introduced for the investigation of a singular interface between the classical and reversible Hopf bifurcations that is theoretically predicted to be generic in nonconservative reversible systems with vanishing dissipation. In particular, such a singular interface exists for the Pflüger viscoelastic column moving in a resistive medium, which is proven by means of the perturbation theory of multiple eigenvalues with the Jordan block. The laboratory setup, consisting of a cantilevered viscoelastic rod loaded by a positional force with nonzero curl produced by dry friction, demonstrates high sensitivity of the classical Hopf bifurcation onset to the ratio between the weak air drag and Kelvin-Voigt damping in the Pflüger column. Thus, the Whitney umbrella singularity is experimentally confirmed, responsible for discontinuities accompanying dissipation-induced instabilities in a broad range of physical contexts.