Can I apply a strain tensor to a shape?

[FlachyJoe]

Does exist a feature to access the equations of (each elements of) a shape, modify them and write a shape from scratch with the new equations?

[dpasukhi]

OCCT is operate with mesh or BREP.
Your approach requires SDF (implicit). That approach is not possible with BREP.
You can only modify underlying geometry parametrisation (plane parameters, sphere parameters and so on)

[FlachyJoe]

Your approach requires SDF

I don't think so: strain tensor is a point-to-point transform and borders of the transformed solid are transformed borders of the initial one.
So mathematical definitions of the initial borders should be enough to define the transformed shape in BREP.
Even if OCC only know basic shapes parameters we should approximate the result by BSplines maybe with the rewrite of the tensor in polynomials.

[dpasukhi]

OCCT do not provide that functionality. You need to write it or find solution in Salome or other products which used OCCT