Shear Modulus from Oscillatory Rheology Calculator

The calculator uses oscillatory shear relationships for sinusoidal stress and strain.

• |G*| = σ₀ / γ₀
• G' = |G*| cos(δ)
• G'' = |G*| sin(δ)
• tan δ = G'' / G'
• ω = 2πf
• |η*| = |G*| / ω
• Parallel plate stress: σ₀ = 2T / πR³
• Parallel plate strain: γ₀ = Rθ / h

Here, σ₀ is shear stress amplitude. γ₀ is shear strain amplitude. δ is the phase angle. G' is the storage modulus. G'' is the loss modulus. |G*| is the complex shear modulus magnitude.

1. Choose the direct stress-strain mode or the geometry mode.
2. Enter the sample name for cleaner exports.
3. Enter the stress amplitude and strain amplitude if they are known.
4. Use the geometry mode when torque, radius, gap, and angular displacement are available.
5. Enter the phase angle measured by the rheometer.
6. Enter the oscillation frequency and select the correct unit.
7. Press the calculate button to view the result above the form.
8. Use the CSV or PDF buttons to download the calculated report.

Why Oscillatory Testing Matters

Oscillatory rheology measures how a material responds to repeated shear. The test applies a small sinusoidal strain or stress. The material answer is also sinusoidal. A phase shift appears when the material stores and dissipates energy. This makes the method useful for gels, polymers, foods, coatings, and pastes.

What the Modulus Values Mean

The complex shear modulus shows the total resistance to deformation. It combines elastic and viscous behavior. The storage modulus, G', describes energy stored during each cycle. A high G' suggests a firm or solid-like structure. The loss modulus, G'', describes energy lost as heat. A high G'' suggests flow, damping, or liquid-like behavior.

Using Phase Angle Correctly

The phase angle connects the complex modulus with its two parts. A low angle means the response is mostly elastic. A high angle means the response is mostly dissipative. Near forty-five degrees, both effects are important. This calculator also reports tan delta. That value is a common damping indicator.

Good Measurement Practice

Use data from the linear viscoelastic region when possible. Large strain may damage the sample structure. Check instrument limits before trusting very small torques. Keep geometry settings consistent between samples. Record temperature, gap, frequency, and sample preparation details. These details improve repeatability. They also help compare batches and formulations fairly.

Interpreting the Result

The result should be treated as a test condition result. Shear modulus can change with frequency, temperature, strain, and aging. A single number rarely describes a complete material. For advanced review, calculate values across a frequency sweep. Then compare curves, crossovers, slopes, and plateaus.