A shape-memory material is one that undergoes a change of crystal structure at a certain temperature called the transformation temperature. Above this temperature the material has one crystal structure (cubic in the case of Cu-Al-Ni) and below this temperature it has another (orthorhombic for Cu-Al-Ni). The low temperature structure of these types of materials allows the material to be easily and apparently permanently deformed. However on heating the material returns to its high temperature structure which has only one possible shape. Thus the material has "remembered" its shape.
If the temperature of the surroundings is above the transformation temperature of a shape-memory material, then the shape-memory effect is not observed, instead the material behaves pseudo-elastically. In this case the low temperature crystal structure can be caused to form by applying stress to the material. Once a sufficient stress is applied to the material, above the transformation stress, the low temperature structure forms and allows the material to under go a large deformation that appears very similar to plastic (permanent) deformation. However on releasing the applied stress the material returns to its original shape with no permanent deformation. The stress-strain response of the material is not linear but is elastic, hence the term, pseudo-elastic.
Here is an example of this type of behavior. Note that the two specimens that did not fracture returned to their original length after a large amount of non-linear deformation.