Step 1: Understanding Perfect Plasticity
A perfect plastic material does not exhibit any elastic behavior. It deforms plastically at a constant stress once yielding begins and continues to do so without any increase in stress. Hence, it lacks an elastic region or strain-hardening.
Step 2: Why it is called "Rigid"
The term "rigid" in this context signifies that the material does not deform elastically (i.e., instantaneously and reversibly), but yields immediately under load and flows plastically at a constant stress level.
Thus, option (A) Rigid best describes a perfect plastic material in idealized mechanical models.