Elastic Strain Energy Calculator
Elastic strain energy is the energy stored in a material under load within the linear elastic regime. It equals half the product of stress, strain, and volume: U = 0.5 * sigma * epsilon * V. For a steel bar with cross section 100 mm^2, length 500 mm, stressed to 200 MPa with E = 200 GPa: epsilon = 200/200,000 = 0.001; V = 100 * 500 = 50,000 mm^3 = 5x10^-5 m^3; U = 0.5 * 200e6 * 0.001 * 5e-5 = 5 J. Enter stress (MPa), strain (dimensionless), and volume (m^3 or mm^3) to compute total strain energy and strain energy density.
Elastic strain energy formula
U = 0.5 * sigma * epsilon * V
u (density) = sigma^2 / (2E) = E * epsilon^2 / 2
U is total elastic strain energy (J). sigma is stress (Pa; note: inputs are in MPa, so 1 MPa = 1 N/mm^2). epsilon is dimensionless strain. V is volume (m^3; note: input is in mm^3, converted by dividing by 10^9). Strain energy density u has units of J/m^3 = Pa.
Applications of elastic strain energy
Elastic strain energy analysis is used to design springs (energy storage capacity), evaluate impact resistance (capacity to absorb energy before yielding), compute deflections in indeterminate structures using Castigliano's theorem, and determine the strain energy release rate in fracture mechanics. The modulus of resilience (yield strength^2 / (2E)) is the maximum strain energy density a material can absorb elastically.
Elastic strain energy: frequently asked questions
What is elastic strain energy?
Elastic strain energy is the potential energy stored in a material due to elastic deformation. When a material is stressed within its elastic range, energy is stored in the distorted atomic bonds. Upon unloading, this energy is fully recovered, driving the material back to its original shape.
What is the formula for elastic strain energy density?
Strain energy density u = 0.5 * sigma * epsilon = sigma^2 / (2E) = E * epsilon^2 / 2. The total elastic strain energy U = u * V, where V is the volume of material under stress. Units are joules (J) or pound-inches (lbf*in).
How is elastic strain energy related to resilience?
The modulus of resilience is the strain energy density stored at the onset of yielding: U_r = sigma_y^2 / (2E). It represents the maximum elastic energy a material can absorb per unit volume without permanent deformation. High resilience is desirable for springs, clips, and snap-fit connectors.
How does strain energy relate to fracture?
In fracture mechanics, crack propagation occurs when the strain energy release rate G (energy released per unit crack area) exceeds the material's fracture energy G_c. The Griffith criterion is the original form of this energy balance, relating critical crack size to fracture toughness.
Can elastic strain energy be calculated for multiaxial stress states?
Yes. For a general stress state, the strain energy density is u = (sigma1^2 + sigma2^2 + sigma3^2 - 2v*(sigma1*sigma2 + sigma2*sigma3 + sigma1*sigma3)) / (2E), using principal stresses. This calculator handles the uniaxial case only.
Official sources
- ASTM E8/E8M, "Standard Test Methods for Tension Testing of Metallic Materials": astm.org.
- NIST, "Fundamental Mechanics of Materials" reference data: nist.gov.
- ASM International, "ASM Handbook Vol. 8: Mechanical Testing and Evaluation": asminternational.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.