What is the relation between stiffness hardness brittleness ductile rigidity and toughness?

Brittleness is the ability of a material to resist permanent deformations while stiffness is the ability of a material to resist elastic (nonpermanent) deformations.

For example, wood, which can bend, is elastic (not stiff) but brittle because you cannot permanently bend wood without compromising the material.

In comparison, steel is highly ductile (nonbrittle) because it can be bent or stretched under load without failure. Thus, even a permanent deformation up to 25% would not result in reduced strenght. It is also less elastic than wood, because it can not bend much without causing a permanent deformation.