It is possible to bend metals but not ionic crystals because of the different bonding in their atomic structures.The valence electrons in metals flow freely between the atoms, while a crystal's electrons have a strong bond with their respective atoms.
The valence electrons are the outermost electrons in atoms. In metals, there is a low attraction between the atoms and their respective electrons, allowing the electrons to float freely around between the atoms. This property also explains why metals conduct electricity, as the floating electrons carry the charge. In ionic crystals, though, each electron is strongly bonded to its atom. Ions form strong bonds that can not be altered without breaking the crystal itself.