Dimensional formula of Strain energy density

How to get the dimensional formula of strain energy density

1. Start from the definition: strain energy density = strain energy / volume.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. displacement = length, so displacement is [L] = [L].
6. work = force × displacement, so work is [M L T^-2] × [L] = [M L² T^-2].
7. strain energy = work, so strain energy is [M L² T^-2] = [M L² T^-2].
8. Put in the dimension of each part: [M L² T^-2] / [L³].
9. Add the powers of each base quantity: [M L^-1 T^-2].

Quantities with the dimensions [M L⁻¹ T⁻²]

• Energy density
• Pressure
• Stress
• Young's modulus
• Bulk modulus
• Shear modulus

Equal dimensions do not make them the same quantity. Compare strain energy density with the others in the full grid.

Three questions on strain energy density

Related quantities

• dP/dx Pressure gradient [M L⁻² T⁻²]
• U Strain energy [M L² T⁻²]
• ε Strain [M⁰ L⁰ T⁰]
• σ Poisson's ratio [M⁰ L⁰ T⁰]
• κ Compressibility [M⁻¹ L T²]
• S Surface tension [M T⁻²]