Rod deformations with possibly irrecoverable corners: Conditions for global injectivity

For rod-type models of slender bodies endowed with active microstructure, such as elongated complex molecules, and different energy classes, we prove existence of minimizing deformations that assure global injectivity under large folding and may describe the occurrence of possibly irrecoverable corners and slips between neighboring cross sections. Atomic measures supported by a finite set enter into play. Eventually, we analyze from a variational viewpoint cases where stresses are constrained to remain in a convex set whose boundary indicates an admissibility threshold.