The nirmaṇakāya in Mahāyāna thought is essentially conceived of as a seemingly physical and tangible manifestation of an otherwise transcendental Buddha. In other words, it is a means through which that transcendental force interacts with ordinary beings in a way they can comprehend. It isn't real or substantial, hence no need for food.
Kumārajīva's ideas are useful to consult here:
Huiyuan 慧遠 (334-416) asked the following question:
《鳩摩羅什法師大義》卷1:「遠問曰。佛於法身中為菩薩說經。法身菩薩乃能見之。如此則有四大五根。若然者。與色身復何差別。而云法身耶。經云法身無去無來。無有起滅。泥洹同像。云何可見。而復講說乎。」(CBETA, T45, no. 1856, p. 122, c6-10)
"Huiyuan asks, 'The Buddha as the dharmakāya teaches sūtras to the bodhisattvas. The bodhisattvas are able to see the dharmakāya. If it is like this, then it would have the four elements and five faculties. If so, what difference is there with a form body, and why call it a dharmakāya? The sūtras state that the dharmakāya is without going and without coming. It has no arising and no cessation, always like nirvāṇa. How are they able to see it and furthermore [how is it] able to teach?'"
Kumārajīva replies to this by introducing the idea of an illusory body.
《鳩摩羅什法師大義》卷1:「什答曰。佛法身者。同於變化。化無四大五根。」(CBETA, T45, no. 1856, p. 122, c11-12)
"Kumārajīva replies, 'The Buddha's dharmakāya is the same as an illusion. It is without the four elements and five faculties.'"
Furthermore...
《鳩摩羅什法師大義》卷1:「如鏡中像。水中月。見如有色。而無觸等。則非色也。化亦如是。法身亦然。又經言法身者。或說佛所化身。或說妙行法身。」(CBETA, T45, no. 1856, p. 122, c20-23)
"Like the image in a mirror or a moon in the water, it appears to have form, but there is no tactile [quality] to it, therefore it is not form. The illusion is also like this. The dharmakāya is also so. Again, the sūtras speak of a dharmakāya, others explain an illusionary body of the Buddha, while others explain it as a dharmakāya of excellent practices."
See here for a bit more related material:
http://huayanzang.blogspot.com/2012/03/ ... mbies.html