Employing ab initio calculations we demonstrate that the complex structural modulations experimentally observed in ultrathin Fe films on Cu(001) originate from Fe bulk phases that arise under extreme deformations. Specifically, we show that the structural modulations correspond to the motifs observed when transforming fcc Fe to bcc Fe in the Pitsch orientation relationship [(001)_{fcc}||(11[over ¯]0)_{bcc}]. The observed structural equivalence between surface and unstable bulk structures naturally explains the experimentally reported magnetic and structural transitions when going from low (two to four MLs) to intermediate (four to ten MLs) film coverages.