John W. Hutchinson’s research while affiliated with Harvard University and other places

Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures.

Experiments are performed on micron-scale single-crystal prototypical structural elements experiencing combined torsion and bending to gather data on their load-carrying capacity in the range of size and strain relevant to micron-scale structures for which little data are available. The observed strengthening dependence on size for the structural elements is in general accord with trends inferred from prior tests such as indentation and pure torsion. In addition, the experiments systematically reveal the strengthening size-dependence of structural elements whose surface has been passivated by a very thin Cr coating, an effect shown to have substantial strengthening potential. A state-of-the-art strain gradient plasticity theory is used to analyze the structural elements over the entire range of size and loading. While the computed trends replicate the experimental trends with reasonable fidelity, the predictive exercise, which is representative of those that will be required in micron-scale structural analysis, brings to light constitutive and computational issues which will have to be addressed before micron-scale plasticity theory can serve as effectively at the micron scale as conventional plasticity does at larger scales.

Curved-sided hexagrams with multiple equilibrium states have great potential in engineering applications such as foldable architectures, deployable aerospace structures, and shape-morphing soft robots. In Part I, the classical stability criterion based on energy variation was used to study the elastic stability of the curved-sided hexagram and identify the natural curvature range for the stability of each state with circular and rectangular rod cross-sections. Here, we combine a multi-segment Kirchhoff rod model, finite element simulations, and experiments to investigate the transitions between four basic equilibrium states of the curved-sided hexagram. The four equilibrium states, namely the star hexagram, the daisy hexagram, the 3-loop line, and the 3-loop "8", carry uniform bending moments in their initial states, and the magnitudes of these moments depend on the natural curvatures and their initial curvatures. Transitions between these equilibrium states are triggered by applying bending loads at their corners or edges. It is found that transitions between the stable equilibrium states of the curved-sided hexagram are influenced by both the natural curvature and the loading position. Within a specific natural curvature range, the star hexagram, the daisy hexagram, and the 3-loop "8" can transform among one another by bending at different positions. Based on these findings, we identify the natural curvature range and loading conditions to achieve transition among these three equilibrium states plus a folded 3-loop line state for one specific ring having a rectangular cross-section with a height to thickness ratio of 4. The results obtained in this part also validate the elastic stability range of the four equilibrium states of the curved-sided hexagram in Part I. We envision that the present work could provide a new perspective for the design of multi-functional deployable and foldable structures.

The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Each of the six segments is a rod having the same length and uniform natural curvature. These rods are bent uniformly in the plane of the hexagram into equal arcs of 120o or 240o and joined at a cusp where their ends meet to form a 1-loop planar ring. The 1-loop rings formed from 120o or 240o arcs are inversions of one another and they, in turn, can be folded into a 3-loop straight line configuration or a 3-loop ring with each loop in an “8” shape. Each of these four equilibrium states has a uniform bending moment. Two additional intriguing planar shapes, 6-circle hexagrams, with equilibrium states that are also uniform bending, are identified and analyzed for stability. Stability is lost when the natural curvature falls outside the upper and lower limits in the form of a bifurcation mode involving coupled out-of-plane deflection and torsion of the rod segments. Conditions for stability, or lack thereof, depend on the geometry of the rod cross-section as well as its natural curvature. Rods with circular and rectangular cross-sections will be analyzed using a specialized form of Kirchhoff rod theory, and properties will be detailed such that all four of the states of interest are mutually stable. Experimental demonstrations of the various states and their stability are presented. Part II presents numerical simulations of transitions between states using both rod theory and a three-dimensional finite element formulation, includes confirmation of the stability limits established in Part I, and presents additional experimental demonstrations and verifications.

The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Each of the six segments is a rod having the same length and uniform natural curvature. These rods are bent uniformly in the plane of the hexagram into equal arcs of 120deg or 240deg and joined at a cusp where their ends meet to form a 1-loop planar ring. The 1-loop rings formed from 120deg or 240deg arcs are inversions of one another and they, in turn, can be folded into a 3-loop straight line configuration or a 3-loop ring with each loop in an "8" shape. Each of these four equilibrium states has a uniform bending moment. Two additional intriguing planar shapes, 6-circle hexagrams, with equilibrium states that are also uniform bending, are identified and analyzed for stability. Stability is lost when the natural curvature falls outside the upper and lower limits in the form of a bifurcation mode involving coupled out-of-plane deflection and torsion of the rod segments. Conditions for stability, or lack thereof, depend on the geometry of the rod cross-section as well as its natural curvature. Rods with circular and rectangular cross-sections will be analyzed using a specialized form of Kirchhoff rod theory, and properties will be detailed such that all four of the states of interest are mutually stable. Experimental demonstrations of the various states and their stability are presented. Part II presents numerical simulations of transitions between states using both rod theory and a three-dimensional finite element formulation, includes confirmation of the stability limits established in Part I, and presents additional experimental demonstrations and verifications.

Curved-sided hexagrams with multiple equilibrium states have great potential in engineering applications such as foldable architectures, deployable aerospace structures, and shape-morphing soft robots. In Part I, the classical stability criterion based on energy variation was used to study the elastic stability of the curved-sided hexagram and identify the natural curvature range for stability of each state for circular and rectangular rod cross-sections. Here, we combine a multi-segment Kirchhoff rod model, finite element simulations, and experiments to investigate the transitions between four basic equilibrium states of the curved-sided hexagram. The four equilibrium states, namely the star hexagram, the daisy hexagram, the 3-loop line, and the 3-loop "8", carry uniform bending moments in their initial states, and the magnitudes of these moments depend on the natural curvatures and their initial curvatures. Transitions between these equilibrium states are triggered by applying bending loads at their corners or edges. It is found that transitions between the stable equilibrium states of the curved-sided hexagram are influenced by both the natural curvature and the loading position. Within a specific natural curvature range, the star hexagram, the daisy hexagram, and the 3-loop "8" can transform among one another by bending at different positions. Based on these findings, we identify the natural curvature range and loading conditions to achieve transition among these three equilibrium states plus a folded 3-loop line state for one specific ring having a rectangular cross-section. The results obtained in this part also validate the elastic stability range of the four equilibrium states of the curved-sided hexagram in Part I. We envision that the present work could provide a new perspective for the design of multi-functional deployable and foldable structures.