C

The work done in stretching an elastic wire per unit volume (strain energy) can be calculated using the relationship between stress and strain. The energy per unit volume, also known as strain energy density, can be expressed as follows:

1. **Strain Energy Density (U) Formula**:
$$ U = \frac{1}{2} \cdot \text{Stress} \cdot \text{Strain} $$

2. **Understanding Stress and Strain**:
- Stress is defined as the force per unit area: $$ \text{Stress} = \frac{F}{A} $$
- Strain is defined as the change in length per unit original length: $$ \text{Strain} = \frac{\Delta L}{L_0} $$

3. **Interpretation**:
The relationship indicates that the strain energy density is directly linked to both stress and strain, leading us to conclude that the correct answer is related to stress and strain as presented in option C. Therefore, option C is the correct representation of strain energy per unit volume.