What formula represents the calculation of strain energy?

The calculation of strain energy is best represented by the formula that incorporates stress and strain in a specific manner. Strain energy can be defined as the energy stored in a material due to deformation and is typically calculated through the relationship of stress and strain.

The formula you referenced, which is half the product of stress and strain, aligns with the area under the stress-strain curve for a material behaving elastically up to the yield point. When stress and strain are plotted, the shape formed is a triangle for small deformations, where the area can be expressed as ( \frac{1}{2} \times \text{(stress)} \times \text{(strain)} ). This triangle represents the amount of energy per unit volume absorbed by the material as it deforms.

In the context of measuring energy, the strain energy per unit volume is therefore calculated using the relationship described, where dividing by two correctly accounts for the linear relationship within the elastic limits of the material. This is why the correct formula involves half of the product of stress and strain, reflecting the triangular shape under the stress-strain curve, accurately representing the strain energy stored in the material.

The other choices either misrepresent the relationship, such as suggesting that strain energy equals