---
title: "Stress–Strain Material Tester Interactive Lab | Sandbox Physics"
description: "What is left in a material after you load it and then take the load off? That depends on the material."
canonical_url: "https://sandboxphysics.com/labs/stress-strain-tester/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/stress-strain-tester/"
last_modified: "2026-10-29"
---

M027 · Solid mechanics

# Stress–Strain Material Tester

**What is left in a material after you load it and then take the load off?** That depends on the material. An elastic specimen returns to its original length, a plastic one keeps a permanent stretch, and a viscoelastic one can hold an internal stress that slowly relaxes. Returning to zero extension does not prove that no stress is stored inside.

Stretch an elastic, plastic, brittle or viscoelastic specimen, hold it, unload it, compress it and bring it back to zero strain. Watch how its internal state and energy change, then estimate the loading slope from the measured force and gauge extension.

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

The specimen deforms uniformly and follows simple small-strain teaching laws. The machine sets the gauge extension exactly, and stress always uses the original area. Necking, contact after fracture, machine compliance and buckling in compression are not modeled, and no real material is certified.

Physics tutorial

## History inside a material

**Background** A loading frame stretches and compresses a specimen. The Lab ties the specimen's geometry to a material model and records force and gauge extension as separate measurements.

**Why it matters** Loading, unloading and careful control of the geometry let you tell competing explanations apart.

Start with the essentials

- **Focus question**: Does zero extension mean no stored stress?
- **One-sentence intuition**: The picture of the specimen, the readouts and the energy record all describe the same physical state.

### Core mathematical model

#### Engineering strain and stress

$$
\begin{aligned}\varepsilon&=\frac{\Delta L}{L_0}\\\sigma&=\frac{F}{A_0}\end{aligned}
$$

Both use the original length and area. The Lab does not compute true stress or follow the shrinking area of a neck.

#### Plasticity with isotropic hardening

$$
\begin{aligned}\sigma&=E(\varepsilon-\varepsilon_p)\\|\sigma|&\leq\sigma_y+H\alpha\\d\alpha&=|d\varepsilon_p|\end{aligned}
$$

Permanent strain can be positive or negative, depending on the direction of plastic flow. Accumulated plastic strain and the yield radius can only grow.

#### A spring in parallel with one Maxwell arm

$$
\begin{aligned}\sigma&=E_\infty\varepsilon+z\\\dot z+\frac{z}{\tau}&=(E_0-E_\infty)\dot\varepsilon\end{aligned}
$$

During a hold, the stress in the transient spring relaxes away. Each constant-rate segment is updated exactly, so a stiff time step cannot distort the result.

#### Work and energy balance

$$
\begin{aligned}W&=V_0\int\sigma\,d\varepsilon\\W&=\Psi+D\end{aligned}
$$

The external work, which can be positive or negative, equals the energy stored elastically and by hardening plus the energy dissipated irreversibly. Energy released at brittle fracture counts as loss.

#### Loading slope from raw data

$$
\begin{aligned}\frac{F_i}{A_0}&\simeq c+\widehat E\frac{\Delta L_i}{L_0}\\0&<\frac{\Delta L_i}{L_0}\leq3\times10^{-4}\end{aligned}
$$

The fit uses only data from the first tensile ramp of a fresh specimen, plus its original geometry. For a viscoelastic specimen the slope depends on the loading rate.

### Common difficulties

#### Where the model stops working

**Typical misconception** If the curve on screen looks smooth, the physics must be right.

**Better mental model** Check whether the state lies inside the range where the model holds, and look at the recorded data. These teaching models do not certify any real specimen.

### Run the experiment

1. 01

   #### Unload after yielding

   Choose Yield and unload, then drag the progress slider through the whole protocol.

   **What to observe:** Bringing the total strain back to zero can take a nonzero stress, because permanent strain remains in the material.

2. 02

   #### Hold extension fixed

   Choose Viscoelastic hold, then change the hold duration and the ramp rate.

   **What to observe:** While the extension is held fixed, the stress relaxes, but the equilibrium spring still carries some tension.

3. 03

   #### Follow the energy released at fracture

   Choose Brittle rupture and look at the energy row before and after the rupture threshold.

   **What to observe:** The stress cutoff cannot be undone. The stored energy it releases shows up as loss, so the energy still adds up.

4. 04

   #### Estimate the loading slope

   Acquire the full protocol, look at the raw channels, export the CSV and change the noise level.

   **What to observe:** The fit on the fresh specimen uses only raw force and extension. For a viscoelastic specimen, the apparent slope changes with loading rate.

Physical conclusion

A model solution, the range where it holds, and an estimate from measured data each answer a different question.

## Related experiments and articles

Fracture mechanics · Reading path

### Fracture mechanics from Griffith’s energy balance to branching cracks

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

1. [Article **Why a crack needs energy to grow**](https://sandboxphysics.com/stories/fracture-mechanics/why-cracks-need-energy/)
2. [Lab **Griffith Criterion for Crack Growth** Grow a crack and track where the work goes](https://sandboxphysics.com/labs/griffith-crack-growth/)
3. [Lab **Photoelastic Stress Viewer** See stress concentrate around a hole](https://sandboxphysics.com/labs/photoelastic-stress-viewer/)
4. [Article **Find the energy release rate from a compliance curve**](https://sandboxphysics.com/stories/fracture-mechanics/energy-release-from-compliance/)
5. [Article **Stress near a crack tip and the stress intensity factor**](https://sandboxphysics.com/stories/fracture-mechanics/stress-near-the-crack-tip/)

Complex fluids · Reading path

### Relaxation, stretching, extension and elastic instability

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

1. [Article **Stress relaxation, creep and the Weissenberg number in a Maxwell liquid**](https://sandboxphysics.com/stories/complex-fluids/stress-relaxation-and-creep/)
2. [Lab **Rotational Rheometer & Couette–Poiseuille Flow** Where a steady viscosity comes from](https://sandboxphysics.com/labs/couette-poiseuille/)

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)