Short note: elastic and plastic behaviour

Elastic behaviour

A material is elastic if it fully regains its original shape and size when the load is removed. Within the proportional limit, stress is proportional to strain (Hooke's law), $\sigma = E\varepsilon$, and the deformation comes from stretching of atomic bonds without any slip of atoms. It occurs below the elastic limit. Steel below its elastic limit is a typical example; rubber is also elastic, but its stress-strain curve is non-linear.

Plastic behaviour

Beyond the elastic limit (yield point), the deformation remains permanently after unloading. It results from slipping of atomic planes by the movement of dislocations. Stress is no longer proportional to strain. Clay, lead and mild steel above yield are plastic.

 stress
   |        ,-----  plastic
   |      ,'
   |    /  <- yield
   |  /  elastic
   +----------- strain
 on unloading, the line returns parallel to the elastic slope,
 leaving a permanent (plastic) strain

Structures are designed to work in the elastic range, while plasticity gives ductility and warning before failure.