  Contraction twinning in magnesium alloys leads to new grains that are
misoriented from the parent grain by a rotation of 56 deg around the a-axis.
The classical theory of deformation twinning does not precise the atomic
displacements and does not explain why contractions twinning is less frequent
than extension twinning. The paper proposes a new model in the continuity of
our previous works on martensitic transformations and extension twinning. A
continuous angular distortion matrix that transforms the initial hcp crystal
into a final hcp crystal is determined such that the atoms move as hard spheres
and reach the final positions expected by the orientation relationship. The
calculations prove that the distortion is not a simple shear when it is
considered in its continuity. The (01-11) twin plane is untilted and restored,
but it is not fully invariant because some interatomic distances in this plane
evolve during the distortion process; the unit volume also increases up to 5%
before coming back to its initial value when the twinning distortion is
complete. Then, the distortion takes the form a simple shear on the twin plane
with a shear direction along the direction [18,-5,-5] and a shear amplitude of
0.358. It is the first time that this twinning mode is reported. Experiments
are proposed to validate or infirm the new model.
