Uniaxial Elastic Strain Energy Density
Calculate elastic energy stored per unit volume in a uniaxial stress state.
Try this formula
Calculate elastic strain energy per unit volume or choose another supported quantity.
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Try this formula
Calculate elastic strain energy per unit volume or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Elastic strain energy per unit volume
Enter the known values to see the result.
Use small strains and a homogeneous, linearly elastic material. Loads are static or slowly applied; remain below the proportional limit. Use uniaxial loading with no other nonzero stress components. This is energy per unit volume, not total energy.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Donney Fan — MECH 360 — Mechanics of MaterialsReference equation: Axial Load — Elastic Strain Energy. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
The area under a linear stress–strain curve is a triangle. Stored energy therefore grows with the square of stress, and remains nonnegative for both tension and compression.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Elastic strain energy per unit volume | ||
| Signed axial normal stress | ||
| Young’s modulus |
Real-World Applications
Resilience
Estimate recoverable elastic energy density.
Energy methods
Supply the local energy density in a loaded bar.
Worked Example
Problem
A uniaxial stress is 100 MPa and E = 200 GPa. Find the stored elastic energy density.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Axial Load — Elastic Strain Energy. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use small strains and a homogeneous, linearly elastic material.
- • Loads are static or slowly applied; remain below the proportional limit.
- • Use uniaxial loading with no other nonzero stress components.
- • This is energy per unit volume, not total energy.
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