No, that's not how the standard mileage method works. The standard mileage method includes allowances for everything -- fuel, maintenance, repairs, depreciation and insurance. The only thing you can add to the standard mileage amount is parking and tolls. If you want to specifically deduct this repair, you would have to use the actual expense method--assuming you have adequate records--and even then, repairs are proportional to vehicle mileage. There is no expense method that allows you to assign 100% of the repair to a business trip even if the damage occurred on a business trip. See chapter 4 in publication 463.
https://www.irs.gov/pub/irs-pdf/p463.pdf