if we are talking about something like 1/8 - 1/2" acyrlic with .040-.080 aluminum laminated to it,as mentioned 3m has an adhesive that I have boight in sheets ,they were an odd size like 22" x 27" if memory serves me correctly. Companies like Briggs & Stratton use it to adhere badges to their products. I have used it to laminate acrylic sheets to brushed aluminum sheets prior to routing dimensional letters, I have multiple projects that have been installed outdoors for 15+ years now that have not failed & are showing no signs of delamination.
the only problems that I have had were from employees skipping steps,not cleaning the substrates properly,not applying pressure etc. Follow proper procedure & I've yet to find a better solution & I spent a good year testing every product that we could find or was recommended when I was producing wholesale dimensional letters years ago.