What characterizes permanent strain in a material?

Permanent strain in a material refers to the condition where the material undergoes a change in shape that is not reversible once the applied stress is removed. This indicates that the material has exceeded its elastic limit, and has entered the plastic deformation phase. In this phase, the internal structure of the material has been altered, leading to a permanent change in shape.

When stress is removed from a material experiencing permanent strain, it does not return to its original shape; instead, it retains the deformed shape. This trait is essential in understanding various materials' behaviors under stress and is crucial in fields such as engineering and materials science where the integrity of materials under load is of utmost importance.

The other characteristics mentioned in the options do not accurately represent permanent strain. For instance, returning to the original shape aligns with elastic behavior rather than permanent strain. Characterizing all materials as behaving solely in a brittle manner overlooks the variety of material behaviors, and an increase in volume does not specifically define permanent strain either. Therefore, the essence of permanent strain is accurately captured by the understanding that a material will undergo a permanent change in shape when stress is applied beyond its elastic limit.