🔬 condensed matter

Yielding behaviour of glasses under shear deformation at constant pressure

This computational study investigates the yielding behavior of glasses under constant-pressure shear deformation, finding that while external pressure quantitatively affects mechanical response and shear band width, the qualitative yielding mechanisms remain consistent with those observed under constant-volume conditions.

Original authors: Krishna K Tiwari, Srikanth Sastry

Published 2026-02-10

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CC BY 4.0

Original authors: Krishna K Tiwari, Srikanth Sastry

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The "Squeezed Sponge" Problem: Understanding How Glass Breaks

Imagine you are holding a dense, heavy sponge. If you squeeze it and then try to twist it, the sponge might change shape, or it might suddenly tear and slip in one specific spot.

Scientists have known for a long time how materials like glass, plastic, or even sand behave when you twist them. However, most of their computer models have a "cheat code": they assume the material stays the exact same size (constant volume) while being twisted.

But in the real world, things aren't that simple. When you twist a material, it often "puffs up" or expands slightly—a phenomenon called dilatancy. This paper, written by Krishna K. Tiwari and Srikanth Sastry, asks a crucial question: "What happens if we let the material breathe (expand or contract) while we twist it, instead of forcing it to stay the same size?"

1. The "Breathing" Material (Constant Pressure vs. Constant Volume)

Think of the difference between a sealed plastic bottle and an open cup of coffee.

Constant Volume (The Sealed Bottle): If you try to squeeze or twist a sealed bottle, the air inside fights back. The pressure inside changes wildly because the volume is trapped. This is how most previous simulations worked.
Constant Pressure (The Open Cup): If you twist a cup of coffee, the surface can move up or down. The "pressure" from the atmosphere stays the same, but the volume of the coffee can change.

The researchers used supercomputers to simulate "glasses" (amorphous solids) under this "open cup" condition. They wanted to see if letting the material expand or shrink would change the way it "yields" (the moment it stops acting like a solid and starts flowing like a liquid).

2. The "Stress Test": Well-Baked vs. Half-Baked

The researchers tested two types of glass:

Well-Annealed Glass (The "Well-Baked Cake"): This is glass that has been cooled very slowly and carefully. It is stable, dense, and tough.
Poorly-Annealed Glass (The "Quick-Baked Cake"): This is glass that was cooled rapidly. It’s a bit messy, less dense, and "unstable."

What they found:
When they twisted the well-baked glass, it held its shape stubbornly until it suddenly "snapped" and expanded. But the half-baked glass was different: it actually got denser (compacted) a little bit before it finally gave way and expanded. It’s like a loose pile of sand that settles into a tight pack before it finally slides apart.

3. The "Shear Band": The Fault Line

When glass fails, it doesn't usually break everywhere at once. Instead, it creates a "Shear Band"—a narrow zone where all the sliding and stretching happens. Think of it like a crack in a sidewalk or a single slip-plane in a deck of cards.

The researchers discovered something fascinating: even when they allowed the material to expand (which usually makes things unstable), these shear bands stayed stable. They didn't just fly apart; they reached a steady width and stayed there.

Even more interesting: The harder you squeeze the material (higher external pressure), the wider these "slip zones" become. It’s like trying to slide two pieces of sandpaper past each other; if you press them together harder, the "messy" area where they grind against each other gets larger.

4. Why does this matter?

If we want to build better smartphones (which use metallic glass), stronger aircraft, or more durable industrial tools, we can't rely on "cheat code" simulations. We need to know how these materials behave when they are allowed to expand and contract in the real world.

The Big Takeaway:
Even though letting the material "breathe" changes the specific numbers (like exactly how much force it takes to break), the fundamental way glass fails remains the same. The "personality" of the glass—how it yields and how it forms those sliding bands—is incredibly robust, whether it's trapped in a box or free to expand.

Technical Summary: Yielding Behaviour of Glasses Under Shear Deformation at Constant Pressure

Authors: Krishna K. Tiwari and Srikanth Sastry
Affiliation: Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), India
Date: February 10, 2026 (as per manuscript)

1. Problem Statement

Traditional computer simulations of the yielding transition in amorphous solids (glasses) typically employ constant volume and strain-controlled protocols. While these methods are computationally efficient, they impose a global constraint on the system's density. In reality, plastic deformation in glasses is intrinsically linked to volumetric effects, such as dilatancy (an increase in volume/decrease in density) associated with plastic rearrangements and the observed reduction of density within localized shear bands.

The authors aim to address this gap by investigating how yielding behavior changes when the system is allowed to undergo volumetric changes under constant pressure conditions. They specifically seek to determine if the qualitative nature of yielding and the stability of shear bands are preserved when the volumetric constraint is relaxed.

2. Methodology

The study utilizes Athermal Quasistatic Shear (AQS) simulations to model the mechanical response of glasses.

Model System: An 80:20 Kob-Andersen binary Lennard-Jones mixture. Simulations were performed for two system sizes: $N = 4,000$ and $N = 64,000$ particles.
Interaction Potential: A Lennard-Jones potential with quadratic corrections to ensure a smooth decay to zero at the cutoff distance ( $r_c = 2.5\sigma$ ).
Sample Preparation (Annealing):
- Poorly Annealed: Prepared via constant volume molecular dynamics at $T = 0.66$ and $\rho = 1.2$ , resulting in an inherent structure energy $e_{IS} = -6.92$ .
- Well Annealed: Prepared via mechanical annealing, resulting in a lower energy $e_{IS} = -7.05$ .
Deformation Protocols:
- Uniform Shear: Incremental strain applied to the system.
- Cyclic Shear: Oscillatory strain varying from $0 \to \gamma_{max} \to 0 \to -\gamma_{max} \to 0$ .
Constant Pressure Implementation: Instead of standard energy minimization used in constant volume AQS, the authors performed enthalpy ($H = U + PV$) minimization at applied reduced pressures of $P = 2, 10^{-3}, \text{ and } -2$ .
Software: All simulations were conducted using the LAMMPS molecular dynamics package.

3. Key Results

A. Uniform Shear Behavior:

Stress-Strain Scaling: While the peak stress ( $\sigma_P$ ) and the slope of the stress-strain curves increase with external pressure, the qualitative shape remains consistent. When stress is rescaled by the peak stress ( $\sigma/\sigma_P$ ), all curves (regardless of pressure or constant volume vs. constant pressure) collapse onto a single master curve.
Density and Energy: The number density ( $\rho$ ) decreases under shear for all pressures, and the energy density ( $U/V$ ) increases with strain. Higher external pressure leads to higher densities and lower energy densities.

B. Cyclic Shear and Yielding Transition:

Annealing Effects:
- Well-annealed glasses show negligible density change before yielding, followed by a discontinuous dilation at the yield point.
- Poorly annealed glasses undergo compaction (increase in density) at low strain amplitudes before eventually yielding and dilating.
Steady-State Properties: Under cyclic shear, the system reaches a steady state. The steady-state density ( $\rho_{ss}$ ) and steady-state energy density ( $U/V_{ss}$ ) both increase linearly with external pressure.
Yielding Signature: A sharp, discontinuous drop in maximum stress ( $\sigma_{max}$ ) is observed at a critical strain amplitude ( $\gamma_{max}^Y \approx 0.10$ ), marking the yielding transition.

C. Shear Band Stability and Dynamics:

Shear Band Width: The authors found that shear bands remain stable under constant pressure. The steady-state width of the shear band increases with external pressure.
Growth Dynamics: The width of the shear band grows following a power law ( $w \sim n^\alpha$ ) after formation, with an exponent $\alpha \approx 0.2$ . This is notably different from the $1/3$ exponent suggested in previous literature.
Local Density: The correlation between plasticity and dilation persists; the number density within the shear band is consistently lower than the average density of the system.

4. Significance and Conclusions

The study provides a critical validation of existing yielding theories by demonstrating that the qualitative phenomenology of yielding is not fundamentally altered by the relaxation of the constant-volume constraint.

Main Conclusions:

Robustness of Yielding Models: The transition from constant volume to constant pressure primarily affects quantitative scales (like stress magnitude) rather than the underlying physics of the yielding transition.
Stability of Localization: Shear bands are robust structures that maintain stability even when the system is allowed to dilate globally.
Pressure-Dependent Scaling: External pressure acts as a scaling factor for stress and influences the steady-state density and shear band width, but the yield strain amplitude remains largely independent of pressure.

Future Directions: The authors suggest that future research should investigate the potential for compositional segregation during volumetric changes and explore anomalous cases like silica, which undergoes compaction rather than dilation during shear banding.