**Explanation:**

The maximum strain energy stored in a material at its elastic limit per unit volume is known as the modulus of resilience. Let's understand the concept in detail:

**Resilience:**
- Resilience is a measure of a material's ability to absorb energy when deformed elastically and then release that energy upon unloading.
- It represents the amount of strain energy stored in a material up to its elastic limit.
- Resilience is given by the area under the stress-strain curve up to the elastic limit.
- Resilience is expressed in terms of stress and strain.

**Proof Resilience:**
- Proof resilience is the maximum energy that can be absorbed by a material without permanent deformation.
- It is the area under the stress-strain curve up to the elastic limit.
- Proof resilience is expressed in terms of stress and strain.

**Modulus of Resilience:**
- The modulus of resilience is the maximum strain energy stored in a material at its elastic limit per unit volume.
- It is a measure of a material's ability to absorb and store energy elastically.
- The modulus of resilience is calculated by taking the integral of the stress-strain curve up to the elastic limit.
- It is expressed in terms of stress and strain.

**Toughness Modulus:**
- Toughness is a measure of a material's ability to absorb energy up to fracture.
- It represents the total area under the stress-strain curve.
- Toughness is given by the integral of the stress-strain curve up to fracture.
- Toughness is expressed in terms of stress and strain.

**Conclusion:**
The modulus of resilience is the correct answer because it specifically refers to the maximum strain energy stored in a material at its elastic limit per unit volume. Resilience, proof resilience, and toughness modulus are related concepts but do not specifically represent this particular measure of strain energy.