English: Often called "superelasticity," the astounding ability of shape memory alloys to survive huge strains without plastic deformation is better labelled "pseudoelasticity."
This animation should help you understand this process.
1. increasing stress causes a stress-induced transformation from austenite to martensite
2. martensite detwins (reversibly) to accommodate the deformation
3. stress is released and the phase transformation from austenite to martensite exactly reverses the previous twinning.