No. One need a specification of the intended behaviour. Behind this specification lays the interface (data type, here a Object-class). This data type on the other hand can have different representations.
Design by contract is a term i didn't read as an agreed scientific term. It is used in OO-languages for some pattern, where you "generate" (read imply) a specification. E.g. two unrelated services use the same data type within their communication. This may be injected or included within their dependencies. To me its related to code generation. It may aid the collaborations between multiple developers across multiple projects to 'move faster'. I have limited and bad experience with this.
> If so, what about invariants? Are invariants related to good interface design?
Invariants in my book are then a synonym for mixins. Which in OO-Design would be represented via dependency inversion. Invariants can be necessary at best. Its no measure for a good interface. If your data types are specified such that invariants do not missbehave, they can be used.
But don't trust me on this.