Prostheses are described for stabilizing dysfunctional sacroiliac (SI) joints. The prostheses are sized and configured to be press-fit into surgically created pilot SI joint openings in dysfunctional SI joint structures. The prostheses include a fixation composition that is adapted to transition from a flowable state, wherein the fixation composition flows into spaces between the prostheses and the dysfunctional SI joint structures when the prostheses are implanted in a dysfunctional SI joint, to a solid elastomer state upon application of radiation energy, wherein the fixation composition forms a positive fit connection by and between the prostheses and the dysfunctional SI joint structures.