A study in Physical Review Letters presents a combinatorial design method for metamaterials: controlling motion states and “frustrated” loops, graded response to pressure, and even matrix-vector multiplication using only mechanical displacements.
A new study by an international team led by Tel Aviv University offers a surprising answer: yes, at least in the mechanical engineering sense. The researchers present a way to design metamaterials so that their structure is not only “strong” or “flexible,” but also able to perform graded responses to stress, and in some cases even perform a useful mathematical operation – matrix-vector multiplication – using only mechanical displacements. This is another step in the burgeoning field of Calculation in material, where the material itself “embodies” logic and calculation, without electronics and without electric current. (arXiv)
The research was led by Prof. Yair Shokef from the School of Mechanical Engineering at Tel Aviv University, and with the participation of undergraduate student Tomer A. Siglov, together with researchers from the Netherlands. The paper describes a “combinatorial” design principle that allows one to build a very large number of movement patterns in a material in advance – like a mechanical Lego set – and decide, using simple geometric rules, which areas will be “free to move” and which will become a kind of rigid trap of stress and deformation.
A “Lego set” of frustrated movement modes and loops
The heart of the work is a proposal of triangular building blocks (in the theoretical model), which can be connected in various ways so that two basic situations are obtained:
- Floppy modes – Deformation patterns that allow the material to “move” relatively easily along certain chains or areas.
- Frustrated loops – Situations where the geometry creates a kinematic mismatch: the material “wants” to deform, but the structure imposes an internal contradiction, so it locks and becomes rigid.
The innovation is not only the identification of these phenomena, but a planning method that allows for the creation of A large number as we wish of such motion states and loops, and also control their spatial shape. This way, it is possible to plan in advance “where the material will fold,” “where it will resist,” and how many motion paths it will have—without relying solely on trial and error or heavy computational optimization.
Gradual response to stress
One of the applications the researchers are demonstrating is Collapse/folding in stages under compression. Instead of a material failing all at once, it can be designed so that one state of motion “opens” and folds first, followed by a second, and so on. The article describes the use of a mechanism of bucking which is also influenced by elasto-plastic properties (i.e. a combination of elasticity with a component of irreversible deformation), to separate the folding stages and produce a controlled response order. Such a property is important for applications such as shock absorption and protection, where energy is desired to be dissipated over time and in a predictable manner.
Material Calculation: Matrix-Vector Multiplication Without Electricity
Here comes the part that explains why the title “Can matter compute?” is not just a metaphor. The researchers show how designing chains and loops in a structure can realize Matrix-vector multiplication: Mechanical displacements are fed into “input” points, and displacements are received at “output” points that are a predefined linear combination of the inputs. This is precisely the heart of the mathematical operation that is used repeatedly in machine learning, signal processing, and physical modeling. The idea is not to replace regular computers, but to open up the possibility of systems in which Calculation in material Done where the forces already exist – for example in soft robotics, passive sensors, or mechanisms that operate without a battery.
More of the topic in Hayadan:
