I first encountered America's strange utterance of "DDDDDDDDD" while watching HetaOni. I was puzzled as heck, as were some other viewers. Then I saw him do it in a couple official Himaruya strips too, as some of that off-to-the-side small text usually used for either background thoughts, onomatopoeia, or otherwise less direct communication.
It seems to be pretty exclusive to the character, and of course trying to google for a varying amount of D's hasn't turned up much luck.
Is it supposed to be an interpretation of our bastardized :D or XD emoticons when we're extremely happy (XDDDDDDD or :DDDDDDD)? Or is there something else to it? Hopefully we can get to the bottom of this mystery someday; it's always best when we can really understand a trademark of our beloved characters.