---
title: "Shear Jamming: Frictional Grains That Lock Without Squeezing Interactive Lab | Sandbox Physics"
description: "Can shearing alone make loose frictional grains carry load? Yes, if the grains have friction and are not too loose."
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language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/frictional-shear-jamming/"
last_modified: "2026-10-30"
---

FR27 · Friction and shear

# Shear Jamming: Frictional Grains That Lock Without Squeezing

**Can shearing alone make loose frictional grains carry load?** Yes, if the grains have friction and are not too loose. Shear at fixed area squeezes grains along one diagonal; with friction, the contacts closed there hold sideways load too, so three contacts per grain suffice instead of four. For 128 model disks at packing fraction 0.81 and friction 0.5, all four test packings carried load within 0.05 strain; frictionless ones still had not by strain 0.3.

Shear 128 frictional disks below the jamming density and watch force chains form along the compressive diagonal, or never form once friction is off.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Two-dimensional disks, half of diameter 1 and half of diameter 1.4, fill a periodic sheared cell at a packing fraction below the point where the same disks jam without friction, about 0.84. Contacts follow the linear spring-dashpot model of Silbert et al. (2001): a push-only normal spring with damping, and a tangential spring two sevenths as stiff that is cut back whenever its force would exceed the friction coefficient times the normal force, so disks can stick, slide and roll. Each step shears the cell by 0.003 and lets the disks come to rest under a small numerical drag, so the shear is slow and quasistatic. Every run starts from a frictionless relaxed packing whose pressure is below a hundred-millionth of the contact stiffness. Gently prepared with the same contacts, as in Shundyak et al. (2007), these disks reach 3.93 contacts each at very low friction and 3.03 at high friction, against the published 3.98 and 3.00. The shear-jamming densities measured on photoelastic disks belong to a different grain and are not reproduced here.

Pressure appears from shear alone

Contacts per disk land between the two isostatic counts

The load runs along the compressive diagonal

More numbers and how they are computed

- **Shear stress now**: $0$
- **Shear stress over pressure**: $0$
- **Contact fabric anisotropy**: $0$
- **Direction contacts favour**: $0$
- **Load-bearing disks**: $0$
- **Share of rattlers**: $0$
- **Strain at which it jammed**: $0$
- **Lowest pressure since the reversal**: $0$
- **Strain steps so far**: $0$
- **Steps that hit the relaxation limit**: $0$
- **Seed**: $0$

Stress is the contact sum $\sigma_{\alpha\beta}=\frac{1}{A}\sum_{c} b_{\alpha}f_{\beta}$, symmetrised, with compression positive; pressure is half its trace and the shear stress resists the imposed shear. The fabric is $R=\langle\mathbf n\mathbf n\rangle$ over the load-bearing contacts; its anisotropy is the difference of its eigenvalues, and its angle is that of the major axis, where $-45^{\circ}$ is the compressive diagonal of this shear.

Physics tutorial

## Jamming by shear alone

**Background** Frictionless disks below their jamming density can be sheared forever without carrying load: they always find a way to slide past each other. Real grains have friction, and friction lets a contact resist sideways as well as head-on.

**Why it matters** Sand, powders and seeds are usually handled below the density at which they would jam isotropically. Whether a gentle shear turns such a material solid decides whether a silo, a chute or a stirred bed keeps flowing.

Start with the essentials

- **Focus question**: Can shearing alone make loose frictional grains carry load?
- **One-sentence intuition**: With friction a contact can hold sideways load, so a packing can stand on as few as three contacts per disk instead of four. Shear squeezes the grains along one diagonal and pulls them apart along the other, and the contacts it closes along the squeezed diagonal are enough to hold. Without friction the same grains slide apart and never carry load at this density.

### Core mathematical model

#### Coulomb limit on each contact

$$
|f_{t}|\le\mu f_{n},\qquad f_{t}=-k_{\mathrm t}u_{t}
$$

The tangential spring $u_t$ stores how far the two surfaces have slid since they touched. When $k_{\mathrm t}|u_t|$ would pass $\mu f_n$, the spring is cut back to the limit and the contact slides (Silbert et al. 2001).

#### How many contacts can hold

$$
z_{\mathrm{iso}}^{0}=2d=4,\qquad z_{\mathrm{iso}}^{\mu}=d+1=3,\qquad n_{m}\le z-(d+1)
$$

Without friction each contact carries one force and each disk has two balance equations; with friction a contact carries two and a disk has three. A contact sliding at the limit adds back one equation, so the mobilised contacts per disk $n_m$ are bounded (Shundyak et al. 2007).

#### Stress from the contacts

$$
\sigma_{\alpha\beta}=\frac{1}{A}\sum_{c}b_{\alpha}f_{\beta},\qquad p=\tfrac12\left(\sigma_{xx}+\sigma_{yy}\right)
$$

The sum runs over contacts, with $\mathbf b$ the vector between the two centres and $\mathbf f$ the full contact force, normal plus tangential. Under shear to the right at the top, the compressive diagonal is $-45^{\circ}$.

### Common difficulties

#### Shear only slides grains past each other

**Typical misconception** Shearing at fixed area cannot squeeze a packing, so it cannot jam it.

**Better mental model** Simple shear at fixed area still compresses along one diagonal. At packing fraction 0.81 and friction 0.5, all four test packings passed the jamming threshold within 0.05 strain; with friction off, none did by 0.3.

#### Once jammed by shear, always jammed

**Typical misconception** A packing that carries load after shearing is now a solid in every direction.

**Better mental model** Reverse the shear and the network built along one diagonal unloads. In the two test packings still loaded at strain 0.15, the pressure fell below the threshold during reverse shear, so by the criterion of Zhao et al. these states are fragile, not shear-jammed.

### Run the experiment

1. 01

   #### Watch load appear

   Open Shear builds force chains and watch the pressure chart and the rose.

   **What to observe:** The pressure starts at zero and climbs as the shear goes on, and the rose grows a long lobe along the dashed diagonal from upper left to lower right: the load runs along the squeezed diagonal.

2. 02

   #### Take friction away

   Choose Frictionless grains just slide.

   **What to observe:** The disks shear just as far, but the pressure stays near zero and no force chains appear.

3. 03

   #### Shear back

   Choose Reverse: the chains let go.

   **What to observe:** Within about 0.06 of reverse strain the pressure falls below the threshold and the rose empties; after about 0.22 a new lobe grows along the other diagonal.

Physical conclusion

Friction lets shear jam grains that are too loose to jam by squeezing, but the solid it makes holds only in the direction it was sheared.

## Related experiments and articles

Granular jamming · Reading path

### From two disks to the jamming point and its memory

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **With friction, how shear jams looser grains**](https://sandboxphysics.com/stories/granular-jamming/friction-and-shear-jamming/)
2. [Lab **Jamming Transition: Squeezing Soft Disks** Use frictionless disks as the control](https://sandboxphysics.com/labs/disk-jamming-compression/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)