Relaxation Modulus Calculator | E(t) Tool

Relaxation Modulus Calculator

Prony Series: E(t), Relaxation Time

Enter initial strain, time, and Prony terms to compute relaxation modulus.

Applied Strain ε₀ (%)

Time t (seconds)

Equilibrium Modulus E∞ (MPa)

Term 1 Modulus E₁ (MPa)

Term 1 Time τ₁ (s)

Term 2 Modulus E₂ (MPa)

Term 2 Time τ₂ (s)

Term 3 Modulus E₃ (MPa)

Term 3 Time τ₃ (s)

Stress Decay

Stress Relaxation

Initial Modulus E(0) = — MPa

Relaxation Modulus E(t) = — MPa

Stress σ(t) = — MPa

Relaxation Ratio E(t)/E(0) = —

The Relaxation Modulus Calculator is a scientifically accurate, interactive tool that computes **relaxation modulus E(t)**, **stress decay**, and **relaxation ratio** using the **Prony series (generalized Maxwell model)**. It simulates **time-dependent stiffness loss** under constant strain. Ideal for **HDPE films**, **PLA mulch**, **greenhouse covers**, and **long-term strain analysis**. Predict stress relaxation with DMA-grade precision. Explore durable polymers at Agri Care Hub.

What is Relaxation Modulus?

**Relaxation modulus E(t)** is stress per unit strain as a function of time:

E(t) = \frac{\sigma(t)}{\epsilon_0}

Units: MPa or GPa. Key components:

E∞: Long-term modulus
Eᵢ: Relaxing moduli
τᵢ: Relaxation times

Learn more on Relaxation Modulus ScienceDirect.

Scientific Foundation: Prony Series

Modulus:

E(t) = E_\infty + \sum E_i e^{-t/\tau_i}

Initial modulus:

E(0) = E_\infty + \sum E_i

Importance of Relaxation Modulus

Critical for:

Mulch films: Tension loss in wind
Pipes: Hoop stress decay
Gaskets: Seal failure
Packaging: Shrinkage
Biodegradable: Shape retention

In agriculture, **low-relaxation mulch** maintains tension — a focus at Agri Care Hub.

User Guidelines

Steps:

Enter constant strain ε₀ (%)
Set time t (seconds)
Input E∞ and Prony terms (Eᵢ, τᵢ)
Click “Calculate Relaxation Modulus”

Use DMA or stress relaxation test data

When and Why to Use

Use when you need to:

Predict HDPE film tension over 1 year
Design wind-stable mulch
Ensure greenhouse film fit
Teach viscoelasticity
Validate biodegradable mulch

Purpose of the Calculator

To make **stress relaxation predictable**. It quantifies **stiffness loss** under strain.

Example: HDPE at 1% Strain

t = 1000 s, E∞ = 100 MPa
E₁=500, τ₁=100; E₂=300, τ₂=10; E₃=200, τ₃=1
E(t) ≈ 380 MPa, σ(t) ≈ 3.8 MPa

Typical Values

HDPE: E(t) drops 50% in 10³ s
LDPE: High relaxation
PP: Moderate
PET: Low relaxation
PLA: Humidity-sensitive

Applications in Agriculture

Relaxation modulus enables:

Tension-stable mulch films
Durable irrigation seals
Long-lasting greenhouse covers
Shape-retaining seed trays

Learn more at Agri Care Hub.

Scientific Validation

Based on:

Maxwell (1867)
Ferry “Viscoelastic Properties of Polymers”
Tscharnuter et al. (2011)
Relaxation Modulus ScienceDirect

Benefits

100% accurate
Prony series
Mobile-friendly
No login
SEO-optimized

Conclusion

The Relaxation Modulus Calculator is your essential tool for viscoelastic polymer design. From lab testing to biodegradable mulch under strain, it delivers **long-term performance**. Start predicting stress decay today with Agri Care Hub.