Bistable domes formed in thin high strength materials create a very thin stiffened structure that bends incrementally and holds its shape.

See more array images (192k).

See text of Metalforming Magazine article.

Overlapping flex-actuated bistable domes offer a simple way to control flexural forces in thin strong flexible materials. They can be used to control springback and create shape memory. They may help reduce stamping and tooling requirements and present opportunities for stronger, lighter construction that could increase fuel efficiency for the transportation industry, for example. They may also aid in prototyping and provide a method for computer modeling of shape.

Descriptions of their use for tactile shape digitizing and flexible pumps that pump when bent can be found through links at, and below.

1) Overview- bistable domes and the effects of overlapping
2) Springback control
3) Creating shape memory
4) Controlling stiffness, flexibility, and rebound in bistable dome materials
5) Thin structures, laminates, sandwiches, composites
6) Small scale production and prototyping
7) Computer modeling
8) Limitations

1) Overview- bistable domes and the effects of overlapping: A flex-actuated bistable dome is a very low profile indentation in thin hard material formed so that when the material around a dome is bent toward the same side as the dome it will buckle and snap toward the outside of the curvature. This simple one-piece structure can be made in a wide range of scale.

Effects of overlapping: Bistable domes with overlapping perimeters are structurally connected and the band of material through their connected perimeters is higher (or lower) in profile toward the centers of the domes. The domes are formed so that this band is structurally longer than the neutral flex axis of the overall structure they form. When the overlapping dome structure is bent this difference creates flexural forces proportional to curvature (see links below for more detailed explanations). The overlapping domes share and neutralize flexural forces by switching sides in numbers proportional to curvature. Their switching patterns reflect location, orientation, and degree of curvature, as long as flexural forces are not absorbed.

Dome characteristics: Bistability can only be created if certain material, dimensional, and formational requirements are met. Dome displacement may not be much greater than the thickness of the material they are formed in. Dome material has to be hard enough so it doesn't absorb the flexural forces that cause switching. Sensitivity to flexure can be controlled by changing material characteristics, relative dimensions, and overlap percentage. Within a range a dome can be equally bistable (equally sensitive to flexure from either side) or have a biased sensitivity for one side.

Minimum radius: When a bistable dome structure made with equally bistable domes is flattened approximately half of the domes will be oriented to one side and half to the other. When all domes are oriented to one side or the other it has reached its minimum radius limits. Minimum radius can be controlled within a range. In between these two states the domes will switch in patterns that reflect the changing shape of the overall multi-dome structure.

2) Springback control: Arrays of closely spaced overlapping flex-actuated bistable domes can provide control of flexural forces that cause springback when shaping thin high strength materials. For example, 1/10 mm thick 300 series spring tempered stainless steel sheet can be pre-shaped with closely spaced overlapping bistable domes to form a stiffer truss-like structure only several times the thickness of the original material that can be shaped and reshaped with little or no springback. Wherever it is bent domes adjust their orientations incrementally, snapping toward the outside of the curvature to neutralize flexural forces and lock in the new shape.

See more array images (192k).

3) Creating shape memory: It is also possible to use bistable dome structures to create localized flexural forces that produce a predisposition or memory for a desired shape. This can be done by managing dome bistability characteristics in patterns and zones. Within physical and minimum radius limits the dome structures force the sheet into a preferred shape. A single row of overlapping bistable domes can be used to force curvature in a band of metal wider than dome diameter.

Dome formation may be done while the sheet is in a flattened state. The bistable domes are forced to adjust to their flattened state patterns during formation but will have a tendency or memory to assume their preferred bistable patterns when released to do so. It may be possible to manage memory strength so that it remains locked in a flattened state until a necessary triggering force is applied.

Simple example: tubular curvature can be created with an axis perpendicular to intermittent parallel rows of bistable domes (and the rollers that may form them).

4) Controlling stiffness/flexibility and rebound in bistable dome materials: Overlapping bistable dome arrays can noticeably stiffen the material they are formed in. When bent, the dome experiencing the greatest concentration of forces (or the weakest dome in the area) will switch first. As the bending motion continues more domes will switch toward the outside of the curvature. Locking domes into one state or another stiffens the structure even more.

Orientation patterns, structures, and shapes may be locked in mechanically or with external coatings during or after formation for permanent stiffening. Coatings with more flexibility could also be used to control stiffness/flexibility and indentation rebound in the overall multi-dome structure or particular zones by controlling the ability of individual domes to switch out of their preferred orientations.

5) Thin structures, laminates, sandwiches, composites: Dome structures are known for their strength. For certain applications interlocking bistable multi-dome structures may prove significantly stronger for their weight than if the original sheet material had been used. Flexibility/stiffness may be controlled with adhesives and fillers that control the ability of a dome to switch. Irregular surface may improve resistance to delamination.

6) Small scale production and prototyping: Preforming with bistable domes can make previously unmanageable materials easier to work with. Generic bistable dome materials may help reduce tooling requirements as well as the need for structural framing and forms. Dome orientation patterns can be locked in with coatings, adhesives, fillers, etc., that determine the stiffness/flexibility of the final shape.

7) Computer modeling: Behavior of overlapping dome structures seems very predictable. It can also be observed that the orientation of a single dome in the middle of hundreds can effect the shape of the whole array. Bistable dome behavior may present an opportunity to model complex curvature of an unstretched plane surface in simple interconnected bistable/digital dome increments.

Note: Making contact switches from bistable domes is probably easier for a single row than for a 2D array. Using overlapping bistable dome rows for sensing shape has been described previously. See link below.

8) Limitations: The bumpiness of dome arrays may only require a thicker than usual coat of finish or it may present a cosmetic problem. Bumpiness may cause air pocketing when using adhesives, etc. A dome array structure may be over-bent to a degree without damage but its functional usefulness is limited to the range between its minimum radius limits. Minimum radius limits are a function of dome characteristics that can be manipulated within a range.

For more on the uses of flex-actuated bistable domes:

Tactile digital bend and shape sensor.
US Patent # 5563458. Apparatus and Method For Sensing Surface Flexure.
Bistable dome pump- a flexible pump that pumps when bent.
US Patent # 6132187. Flex-actuated Bistable Dome Pump.

Unpatented. For information and prototyping assistance contact:

Paul Ericson: