🔬 condensed matter

Cooking crystalline candies and the ductile to brittle transition in concentrated suspensions

This paper demonstrates that the ductile-to-brittle transition observed in concentrated non-Brownian suspensions, such as fudge and calcite particle mixtures, is driven by increasing solid volume fraction and is sensitive to boundary conditions.

Original authors: Andreia F. Silva, James A. Richards, Fiona Jeffrey, Rory E. O'Neill, Daniel J. M. Hodgson, Christopher Ness, Wilson C. K. Poon

Published 2026-05-08

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CC BY 4.0

Original authors: Andreia F. Silva, James A. Richards, Fiona Jeffrey, Rory E. O'Neill, Daniel J. M. Hodgson, Christopher Ness, Wilson C. K. Poon

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

Imagine you are making a batch of fudge. You start with a pot of sugar, milk, butter, and syrup. As you boil it, the water evaporates, and the sugar concentration gets higher and higher. You might think this is just about making a tasty treat, but this paper reveals that your candy pot is actually a secret laboratory for studying how materials break.

The researchers discovered that by simply changing how long you boil the fudge (or how hot you let it get), you can turn the mixture through three distinct "personality" changes:

The Runny Soup: At lower temperatures, the mixture is still a thick, flowy liquid.
The Play-Doh: As you boil it a bit more, it turns into a soft, squishy solid. If you squeeze it, it deforms and stretches without breaking. This is called ductile.
The Glass: If you boil it even longer, it becomes a hard, stiff solid. But here's the twist: if you squeeze it, it doesn't bend; it shatters. It snaps suddenly with a loud crack. This is called brittle.

The "Crowded Room" Analogy

Why does this happen? The authors explain it using the idea of a crowded room.

The Liquid Phase: Imagine a room with only a few people. They can walk around freely, bumping into each other occasionally but mostly flowing past one another. This is like the sugar crystals floating in the water.
The Ductile Phase: Now, pack the room with more people. Everyone is touching their neighbors. If you try to push the crowd, they can't walk away, but they can shuffle and slide past each other. They deform together, like a mosh pit that moves as a single unit. This is the "ductile" stage.
The Brittle Phase: Finally, pack the room until it is absolutely jammed. There is zero space to move. If you push on one side, the pressure has nowhere to go but straight through. Instead of shuffling, the crowd suddenly snaps apart in a jagged line. This is the "brittle" stage.

In the fudge, the "people" are sugar crystals, and the "room" is the water, fat, and protein. As you boil off the water, the crystals get more crowded (the volume fraction increases), forcing the material to switch from squishy to shattering.

The Titanic Connection

The paper mentions a famous historical event to explain why this matters. The Titanic sank in 1912 partly because the steel used to build it became brittle in the freezing cold water. Just like the fudge, the steel underwent a "ductile-to-brittle transition." In cold temperatures, the metal atoms couldn't slide past each other, so the ship's hull snapped like a dry twig instead of bending.

The researchers wanted to know: Does this happen in other messy, crowded materials, not just metals?

The "Calcite" Experiment

To prove this isn't just a weird sugar thing, they made a second material: a paste of calcite powder (a type of limestone) mixed with a thick liquid. They didn't boil this one; instead, they just added more and more powder to the liquid.

The result was identical to the fudge:

Low powder = Flowing liquid.
Medium powder = Squishy, bendable solid.
High powder = Hard, snapping brittle solid.

This suggests that the rule is universal: Any crowded mixture of tiny, non-moving particles will eventually go from bendy to breakable if you pack them tight enough.

The Computer Simulation

The team also used a computer to simulate millions of tiny balls bouncing around. They found that the "snap" happens because the forces inside the material become more evenly spread out.

In the bendy phase: The pressure is uneven. Some particles are carrying huge loads while others carry nothing. The material can "wiggle" to relieve this stress.
In the snapping phase: The pressure is spread out so evenly that the whole structure is under tension at once. When it finally gives way, it gives way all at once, causing a sudden fracture.

The "Boundary" Surprise

One interesting finding is that how you squeeze the material changes how it breaks.

In the real world (like in their lab machine), the fudge and calcite paste snapped with a visible crack at a 45-degree angle.
In the computer simulation, where the "walls" of the box were invisible and didn't let the material expand, the material didn't snap as dramatically.

This teaches us that how you hold a material matters. The way a material breaks depends not just on what it's made of, but on the rules of the container it's in.

The "Mouthfeel" Connection

Finally, the paper notes that the force required to break the "brittle" fudge is exactly the kind of pressure your mouth uses when chewing. This helps explain why some fudges feel like they "melt" or "crunch" in your mouth, while others feel like hard candy that shatters. It's all about that transition from squishy to snap.

In short: By studying how fudge and rock paste break, the scientists found a universal rule for how crowded, messy materials behave. If you pack them tight enough, they stop bending and start breaking.

Technical Summary: Cooking crystalline candies and the ductile to brittle transition in concentrated suspensions

Problem Statement
The ductile-to-brittle transition (DBT) is a well-documented phenomenon in metals and polymers, with significant implications for structural integrity (e.g., the Titanic disaster) and seismology. While recent interest has focused on amorphous non-polymeric soft materials (e.g., soft glasses, fibrous networks), the DBT in particulate suspensions remains under-explored despite the ubiquity of such materials in applications ranging from concrete to chocolate. Specifically, the origin of the DBT in non-Brownian suspensions and pastes is not well understood. This study investigates whether a DBT exists in concentrated suspensions and identifies the driving mechanisms, using confectionery (fudge) and model calcite suspensions as experimental systems.

Methodology
The authors employed a multi-faceted approach combining experimental rheology, compression testing, and particle-based simulations:

Fudge Preparation and Characterization:
- A "minimal recipe" of sucrose, condensed milk, golden syrup, and butter was heated to specific final cooking temperatures ( $T_{cook}$ ) ranging from 108°C to 120°C.
- Increasing $T_{cook}$ drives off more water, increasing the final sucrose concentration ( $c_f$ ) and, consequently, the volume fraction of sucrose crystallites ( $\phi$ ) upon cooling and crystallization.
- $\phi$ was estimated theoretically based on solubility data and density, ranging from $\phi \approx 0.51$ (108°C) to $\phi \approx 0.58$ (120°C).
- Samples were subjected to uniaxial compression in a universal testing machine to record force-displacement curves and observe fracture modes. Shear rheology was performed on lower- $\phi$ samples to characterize fluid-solid transitions.
Calcite Suspension Model:
- To isolate the effect of solid volume fraction from complex chemical interactions (e.g., Maillard reactions in fudge), suspensions of non-Brownian calcite powder in a glycerol-water mixture were prepared.
- The solid volume fraction ( $\phi_c$ ) was directly controlled from 0.48 to 0.60, spanning the frictional jamming point ( $\phi_\mu$ ) to random close packing ( $\phi_{rcp}$ ).
- These samples underwent identical compression protocols to the fudge.
Computer Simulations:
- Discrete Element Method (DEM) simulations using LAMMPS modeled 2000 frictional, adhesive spheres under biaxial extension (uniaxial compression).
- Simulations explored the stress response and contact force distributions across volume fractions ( $\phi_s$ ) from 0.57 to 0.65 under periodic boundary conditions.

Key Results
The study identifies a sequential transition in mechanical behavior as the solid volume fraction increases:

Fluid-to-Solid Transition: Both fudge and calcite suspensions exhibit a transition from a fluid state to a ductile solid state near the frictional jamming point ( $\phi_\mu \approx 0.52$ for calcite; $\phi \approx 0.52$ for fudge at $T_{cook} \approx 110^\circ$ C).
Ductile-to-Brittle Transition (DBT): As $\phi$ $ϕ$ increases further, a distinct DBT is observed.
- Fudge: At $T_{cook} = 117^\circ$ C ( $\phi \approx 0.56$ ), the material transitions from ductile (gradual compression, barrel formation) to brittle (abrupt stress drop, 45° shear fracture, and axial splitting). The brittle regime is characterized by a "stress overshoot" followed by a sharp drop in force.
- Calcite: A similar transition occurs between $\phi_c = 0.54$ (ductile) and $\phi_c = 0.56$ (brittle). At higher fractions ( $\phi_c \le 0.60$ ), the material becomes increasingly stiff and brittle.
Simulation Insights:
- Simulations confirm the transition from fluid to ductile solid and the emergence of a stress overshoot at high $\phi$ .
- However, simulations under periodic boundary conditions show a stress plateau after the overshoot, whereas experiments show a catastrophic stress drop. The authors attribute this discrepancy to boundary conditions: the experimental stress drop is caused by macroscopic fracture (45° cracks and axial splitting), which is suppressed in constant-volume periodic simulations.
- Microscopically, the DBT correlates with a homogenization of the stress distribution. As $\phi$ increases from $\phi_\mu$ to $\phi_{rcp}$ , the distribution of contact forces becomes more uniform, and the proportion of high-force contacts (force chains) decreases.

Key Contributions

Demonstration of DBT in Suspensions: The paper provides the first experimental evidence of a DBT in concentrated non-Brownian suspensions, demonstrating that the phenomenon is generic across different material systems (sugar crystals in a complex matrix and inorganic calcite powder).
Mechanism Identification: The study proposes that the DBT is driven by the increasing solid volume fraction, which reduces stress inhomogeneity as the system moves from frictional jamming toward random close packing. This aligns with theoretical models of annealed soft glasses.
Role of Boundary Conditions: The work highlights that the observational signature of the DBT (specifically the magnitude of the post-yield stress drop) is highly sensitive to boundary conditions. Macroscopic fracture in experiments creates a distinct "brittle" signature that is absent in periodic simulations, despite the underlying physics of yielding being similar.
Plastic Deformation Scaling: By comparing simulation peak stresses with experimental data, the authors deduce that the peak stress in these brittle suspensions is governed by the plastic compressive strength of the individual particles, rather than purely elastic deformation.

Significance and Claims
The authors claim that their findings contribute to a fundamental understanding of the mechanical response of concentrated suspensions. They posit that the DBT in these materials is not an anomaly but a generic feature of the transition from frictional jamming to random close packing, driven by the homogenization of stress fields.

Practically, the study bridges the gap between soft matter physics and food science. The peak stress observed in the brittle fracture of fudge ( $\sim 0.1$ MPa) falls within the range of forces applied in the human mouth during mastication. The authors suggest that understanding the DBT and the complex yielding behavior of such materials is crucial for predicting and designing the "mouthfeel" of confectioneries, an area where viscosity is traditionally the primary metric.

The paper concludes modestly, noting that while the correlation between stress homogeneity and the DBT is supported by contact force distributions, direct probes of collective microscopic yielding events and stress propagation in jammed frictional materials are required to fully confirm the proposed mechanism.