Yes. In North America, shredded, ripped up, and ripped to pieces are equivalent here. Rip has a primary meaning to tear or to cut. Rip up and ripped to pieces have a primary meaning of torn into pieces. Shredded is equivalent to torn into pieces (and of ripped to pieces). Shred has the synonyms of tear up and rip up. Online Collins Dictionary shred https://www.collinsdictionary.com/dictionary/english/shred verb If you shred something such as food or paper, you cut it or tear it into very small, narrow pieces. They may be shredding documents. [VERB noun] Finely shred the carrots, cabbage and cored apples. [VERB noun] Synonyms: TEAR UP, RIP UP, cut up, mince More Synonyms of shred rip up https://www.collinsdictionary.com/dictionary/english/rip-up phrasal verb If you rip something up, you tear it into small pieces. If we wrote I think he would rip up the letter. [VERB PARTICLE noun] She took every photograph of me that was in our house and ripped it up. [VERB noun PARTICLE] rip https://www.collinsdictionary.com/dictionary/english/rip verb When something rips or when you rip it, you tear it forcefully with your hands or with a tool such as a knife. I felt the banner rip as we were pushed in opposite directions. [VERB] I tried not to rip the paper as I unwrapped it. [VERB noun] Synonyms: be torn, tear, split, burst More Synonyms of rip

A shred has specific shape: https://www.thefreedictionary.com/shred A rip is more random. I wouldn't use "shredded" there as it already presupposes pieces of a certain shape unless you remove the word "pieces".