In the previous context of the sentence below the disaster that caused the damage and displacement of people is clearly identified and I'd like to avoid repeating it again, but I'd still like to specify that I'm referring to the "damage at hand" caused by an event that is being talked about:
After people have been taken care of, the team focused its efforts on repairing the damage sustained/incurred
Damage incurred sounds better to me, and I was also thinking about inflicted, but I'm not sure whether this word is applicable if the damaged object referred to is not human.
And my other question about this is whether putting incurred in front of the noun damage works here: "…repairing the incurred damage"
Best Answer
Consider the definitions:
If the damage was malicious (someone else purposely caused the damage), then you might the damage was inflicted on them. If they brought the problem on themselves, then you can talk about the damage incurred. If the damage was caused by a natural catastrophe, it was simply damage sustained by them.
The terms damage incurred and damage suffered may also be contrasted in a legal sense, as described in the article When Does "Incurred" Mean "Incurred" for Insurance and Reinsurance Purposes? by Larry Schiffer. Note that the term damage may have a more narrow / specialist legal definition here than in the usage described in the paragraphs above.