Crucial insights about memory formation in glassy materials (disordered solids) under random deformation

Amorphous materials such as glass are solids whose internal structure lacks a repeating pattern. Their molecules are arranged in a random and irregular way. Surprisingly, these disordered materials can ‘remember’ past mechanical experiences, i.e., the way they respond to a force can depend on how they have responded to external forces before.

Roni Chatterjee and Smarajit Karmakar at the Tata Institute of Fundamental Research, Hyderabad in collaboration with Damien Vandembroucq (CNRS, ESPCI Paris, France) and Muhittin Mungan (Heinrich Heine University Düsseldorf, Germany) report crucial insights on memory formation in amorphous solids. This study reveals that amorphous materials can encode memories even when the applied deformations are completely random rather than perfectly periodic, challenging the conventional understanding of memory formation in disordered solids. The findings of this study have been published in the New Journal of Physics.

Researchers usually study this kind of memory in very controlled laboratory conditions. They repeatedly deform a material in a regular, predictable way, gently shearing it back and forth over many cycles. Over time, the material ‘learns’ this pattern and settles into a state that reflects its past training. This has been the standard way to understand memory in such systems.

Roni Chatterjee draws an example of the repetitive deformation experienced in a new pair of shoes. New shoes often feel stiff and uncomfortable, at first. However, after continuous use, they gradually adjust to the shape of the feet. Eventually, they feel just right; as if they “remember” your foot shape. An intriguing aspect is that this adaptation does not happen because the feet move in a perfectly repeated way - these movements are irregular and unpredictable; walking fast, sometimes slowly, sometimes twisting and turning. Yet, despite this randomness, the shoes still adapt.

This everyday observation raises an important question: Do materials really need perfectly repeated deformation to form memory, or can they learn even from random experiences?

To explore this, the TIFRH team studied the mechanical response of a simplified version of a disordered material (for example: glass) using computer simulations. Instead of deforming it in a perfectly repeated way, they introduced randomness. They let the material deform repeatedly in an irregular, unpredictable way, but within a fixed limit (deformation amplitude). One may think of this like gently pushing and pulling something randomly, while making sure it never moves too far (beyond the amplitude) in either direction.

The researchers “trained” the material by repeatedly applying this random deformation with a fixed amplitude over many cycles. After training, they performed a “read-out” step: they applied a single, controlled cycle of deformation and measured how much the material changed compared to its trained state.

When an amorphous material is subjected to random deformation of a given amplitude, for example, 5% strain over 100 cycles, it gradually evolves into a characteristic state associated with that driving condition. To determine whether the material has retained a memory of this training amplitude, the researchers performed a series of “read-out” deformations at different amplitudes, 1%, 2%, 3%, and so on. After each single read-out cycle, they compared the resulting read-out state with the trained state. To quantify the difference between the two states, they measured how much the particles had moved relative to one another, a quantity known as the mean squared displacement. Remarkably, the displacement vanished only when the read-out deformation amplitude matched the original training amplitude of 5%. In other words, the material returns to the same state only when the read-out amplitude matches the training amplitude. This demonstrates that the material retains a precise memory of the deformation amplitude it experienced during training, even under random driving conditions.

They also found an important limit to this behavior. Memory forms only when the training deformation is below a certain threshold, known as the yielding point, beyond which the material starts to break or flow permanently. If the deformation is too large (above this yielding point), the memory is lost.

Their results show that disordered materials do not need perfectly regular training to form memory. Even under random, irregular deformations - much like what happens in everyday life - these materials can still learn and remember. This brings scientific understanding a step closer to real-world conditions, where randomness is the norm rather than the exception.

[Content: Roni Chatterjee]