Word for eating things that aren't food

Is there a word for trying to eat things that aren't food?

I'm thinking particularly in the context of babies, where it's a normal part of the learning process, but I dare say it is a disorder that can occur later in life too.

My own punt at a word was panphagia, but that turned out to be a dinosaur...

pica from Oxford Dictionaries Online

[MASS NOUN] Medicine

A tendency or craving to eat substances other than normal food (such as clay, plaster, or ashes), occurring during childhood or pregnancy, or as a symptom of disease:

• This tendency was aggravated by apparent pica (an abnormal craving) that prompted him at various times to inhale the terpene camphor and to ingest other products containing terpenes, namely his oil paints and turpentine.

• Some pregnant women, for example, have stopped eating nonfood items after they were treated for iron deficiency anemia, a common condition among pregnant women with pica.

• Rarely, a person with iron-deficiency anemia may experience pica, a craving to eat nonfood items such as paint chips, chalk, or dirt.

Allotriophagia fits your question, but hyperorality fits your elaboration upon it.

Allotriophagia is an obscure word (most dictionaries don't list it, but you will find it mentioned in medical and veterinary works if you do a book search) because generally if someone is actually engaging in allotriophagia then they have pica which is a condition of which allotriophagia is a symptom.

Allotriophagia is also used to refer to the condition, but pica is a lot shorter so even doctors and vets, generally no cowards in the face of a long word of Greek origin, seem to often prefer it.

But for the actual act of such eating itself, only allotriophagia is used.

It does not however cover infants' tendency to put a lot of things in their mouths; any ingestion is incidental so it's not an act of eating. (It would be a reasonable figurative use perhaps, but for allotriophagia being probably too obscure for a figurative use to do any useful conjuring in the minds of an audience).

A compulsion to put something into your mouth (which could lead an adult to behave like an infant in this regard) is hyperorality. It could be combined with or seprate from allotriophagia or hyperphagia (compulsively eating a lot, but generally restricted to food).