We define what is a generic separating set of invariant functions (a.k.a. a
weak functional basis) for tensors. We produce then two generic separating sets
of polynomial invariants for 3D elasticity tensors, one made of 19 polynomials
and one made of 21 polynomials (but easier to compute) and a generic separating
set of 18 rational invariants. As a byproduct, a new integrity basis for the
fourth-order harmonic tensor is provided
