Using the same data, calculate the strain energy density U given σ = 25 MPa and ε = 0.00139. Which value is closest to the result?

Using the same data, calculate the strain energy density U given σ = 25 MPa and ε = 0.00139. Which value is closest to the result?

• A. 0.0174 kJ/m^3
• B. 174 kJ/m^3
• C. 2.75 kJ/m^3
• D. 17.4 kJ/m^3

Answer: (D)

Key idea: in linear elastic materials under uniaxial loading, the strain energy density (energy stored per unit volume) is U = ∫0^ε σ dε = 1/2 σ ε. This comes from integrating the stress over the strain during loading, and using σ = Eε for a linear material. Plugging in the numbers: U = 0.5 × 25 MPa × 0.00139 ≈ 0.017375 MPa. Since 1 MPa = 10^6 N/m^2, this is 0.017375 × 10^6 J/m^3 ≈ 1.7375 × 10^4 J/m^3 ≈ 17.4 kJ/m^3. So the result is about 17.4 kJ/m^3.

Key idea: in linear elastic materials under uniaxial loading, the strain energy density (energy stored per unit volume) is U = ∫0^ε σ dε = 1/2 σ ε. This comes from integrating the stress over the strain during loading, and using σ = Eε for a linear material.

Plugging in the numbers: U = 0.5 × 25 MPa × 0.00139 ≈ 0.017375 MPa. Since 1 MPa = 10^6 N/m^2, this is 0.017375 × 10^6 J/m^3 ≈ 1.7375 × 10^4 J/m^3 ≈ 17.4 kJ/m^3. So the result is about 17.4 kJ/m^3.