**Core Concept**
The question is testing the concept of viscoelasticity in elastomers, which refers to the ability of materials to deform under stress and recover their original shape when the stress is removed. In this context, permanent deformation following strain in compression is a concern, particularly in medical devices such as implants and catheters.

**Why the Correct Answer is Right**
The correct answer is based on the principle of viscoelastic creep, where elastomers subjected to constant stress will eventually undergo permanent deformation. This is due to the rearrangement of polymer chains and the formation of permanent bonds between them. The rate of creep is influenced by the material's molecular structure, temperature, and the magnitude of the applied stress.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not follow the expected order of increasing permanent deformation. Elastomers tend to exhibit a range of behaviors, including elastic recovery, viscoelastic creep, and plastic deformation, depending on the magnitude and duration of the applied stress.

**Option B:** This option is incorrect because it suggests that elastomers exhibit a sudden transition from elastic to permanent deformation. In reality, the transition from elastic to permanent deformation is gradual and influenced by various factors, including the material's molecular structure and the magnitude of the applied stress.

**Option C:** This option is incorrect because it implies that elastomers can withstand extremely high levels of stress without undergoing permanent deformation. While some elastomers may exhibit high elastic recovery, they will eventually undergo permanent deformation when subjected to excessive stress.

**Option D:** This option is incorrect because it suggests that elastomers exhibit a linear relationship between stress and permanent deformation. In reality, the relationship between stress and permanent deformation is complex and influenced by various factors, including the material's molecular structure and the magnitude of the applied stress.

**Clinical Pearl / High-Yield Fact**
When working with elastomers in medical devices, it's essential to consider their viscoelastic properties to avoid permanent deformation and ensure reliable performance over time. This can be achieved by selecting materials with optimal molecular structures and designing devices that minimize stress concentrations.

**Correct Answer: C. Elastomers exhibit a range of behaviors, including elastic recovery, viscoelastic creep, and plastic deformation, with plastic deformation typically occurring at higher levels of stress.