The transformation of olivine to spinel in a subducting slab gives rise to
thermal strain, transformation strain, and buoyancy forces inside the slab.
We use a finite element method to solve the mechanical equation, and we fo
llow the evolution of the stresses inside the slab during its descent. We u
se two different rheologies: elastic and viscoelastic with a viscosity that
depends on pressure, temperature, and grain size. The stresses due to buoy
ancy are found to be negligible compared to the internal stresses due to th
e phase transformation. When the viscoelastic rheology is used, a zone of v
ery high differential stress coincides with the olivine-spinel phase bounda
ry. This zone is associated with large downdip compressive stresses inside
the metastable olivine wedge, and large downdip tensile stresses in the spi
nel region, along the wedge. If we assume that the failure criterion can be
related to the differential stress, our model is in agreement with the pat
terns of deep seismicity. However. patterns of deep seismicity are unlikely
to reflect buoyancy stresses, which in the presence of a metastable olivin
e wedge, are negligible compared to the internal stresses.