John: subject (noun)
tends to get hungry: predicate
tends to get: head of the predicate (verb phrase)
hungry: predicative, subjective complement or subject complement [all 3 terms mean the same] (adjective)
Randolph Quirk considers "tend to" a semi-auxiliary verb. This would make "get" (a linking verb) the main verb in the verb phrase. It can't possibly take a direct object. There are other verbs that act similarly to tend to: try to, happen to, fail to, etc.
Hope that helps, even though my answer comes late.
Miriam