Relationship between "ductile" and "malleable"

What is the relationship between the words ductile and malleable? They are definitely not antonyms, but can we call them synonyms?

Both words indicate an item can be shaped, as in metal or plastic, but you would not say a child's mind is ductile, because you don't hammer at a child's mind, or heat it to mold it into shape. Malleable is a more flexible word.

Ductile has the property of physical shaping, while malleable has the property of formation. Malleable can include shaping by force, as in using a mallet. But malleable also could allow change through influence or subtle alteration as opposed to force: The child is malleable, so be careful what you teach him. Ductile allows only physical change of shape: I must heat the plastic to make it ductile.

Ductile is also related to the word viscous or viscosity, because a solid that flows is ductile. Viscous lava can be shaped through physical means, but the more viscous it is, the less fluid the lava is, and the more force required to change its shape. So highly viscous fluid is less ductile than low viscosity lava. Low viscosity lava is malleable. (Easily shaped.) High viscosity lava is ductile. (Resistant to shaping, but it is possible to use force or its physical properties to make it easier to shape a ductile material.)

see the Wikipedia entry on ductility.

[D]uctility is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire. ... Malleability, a similar property, is a material's ability to deform under compressive stress.