Yes, some dinosaurs did have self-sharpening teeth, such as the ornithopods and ceratopsians. Both were members of the Cerapoda group, all of which had cheek teeth with thickened enamel on one side only. The other side of the teeth—the actual surface used to chew the plants—had only the softer dentine. As the animal chewed, the upper and lower teeth ground against each other, with the softer dentine wearing away faster than the harder enamel. This made these dinosaur teeth self-sharpening.