Researchers at the Hebrew University of Jerusalem have discovered that a surface can withstand all local geometric conditions—and yet reach a global threshold beyond which it cannot remain smooth. The result may help in understanding shapes in nature and designing shape-shifting materials.
A leaf, petal, or growing tissue does not always expand like a smooth balloon. Sometimes they suddenly develop dimples, folds, andwrinklesNew research by Dr. Yifei Zhang, Prof. Michael Moshe and Prof. Eran Sharon From the Institute of Pharmacy toPhysics The Hebrew University offers a new geometric explanation for this.
As a sheet grows, each area of it tries to have a certain length and curvature. If the requirements are not in harmony with each other, a "Geometric frustration": The material cannot assume the desired rest shape without stretching, compressing, or bending.
Until now, it was customary to check suitability mainly through local conditions - whether each small area of the surface can receive theגאומטריה The new study shows that such testing is not always enough. Each small piece may pass the familiar tests, but the entire surface will not be able to exist smoothly.
Through mathematical analysis, computer simulations, and experiments with elastic envelopes, the researchers found that the accumulation of curvature can reach a certain threshold. Beyond this threshold, a global mismatch appears: the surface cannot continue to grow isometrically—that is, without stretching the material—and so it transitions to a wrinkled state.
Instead of deforming in a completely random manner, the sheet forms an orderly array of cone-shaped dimples. The folds allow it to reduce the strain that has accumulated in it and fulfill at least some of the growth requirements.
One of the striking results was that a single cut in the sheet removed the restriction and allowed it to return to a smooth shape. The cut does not fundamentally change the properties of the material itself, but it does change the connectivity of the surface. From this, the researchers concluded that the origin of the phenomenon is topological and global, and not a local defect in the material.
The principle could help understand the formation of complex shapes in plants and biological tissues. It could also become a design tool: if engineers knew at what threshold collapse occurs and what pattern would form, they could program sheets to fold or change shape in a controlled manner.
Possible applications include soft robots, medical devices that deploy inside the body, foldable components for space, andMetamaterials Mechanical. However, the current research deals with the basic physical principle; translating the principle into an engineering product will require further research.
Questions and Answers
What is geometric frustration?
Answer: A situation in which the geometric requirements imposed on a material cannot coexist without tension, compression, or wrinkling occurring.
What's new in the discovery?
Answer: It shows that a mismatch can be global and topological, even when every small area of the surface meets the familiar local conditions.
Why does a single cut smooth the surface?
Answer: The cut changes the topological connectivity and eliminates the global constraint that has accumulated in the sheet.
Does the phenomenon only appear in artificial materials?
Answer: No. The same principle may participate in the design of leaves, flowers, and growing tissues.
More of the topic in Hayadan:
- Can matter compute? “Mechanical Lego” from Tel Aviv University
- A method for designing mechanical metamaterials using induced defects
- The future is changing shape
- Electromagnetic structure based on topological connections
- Discovery sheds light on the mystery of the glass passage
For the original publication: Opening the original publication
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Pretty
Now they will explain how dirt roads are paved.
Become corrugated