Dear Dr. Chavarria-Krauser,

Thank you very much for your comment.

In fact, to receive smooth solutions at the interface, equations for different geometries should be connected by gluing conditions equating the forces and deformations on each side: σn = σ' n' and u = u', where n denotes the exterior normal to the boundary.

However, in first approximation we let both subdomains be weakly coupled (in visco – plastic phase) when cyclic wall building processes take place, and strongly coupled mechanically
(in visco – elastic phase) when wall building processes expire and the equations start to be valid. We consider only the radial part of the stress σrr and strain u_rr = ∂_ru_r tensors in the transition zone, ignoring shear stresses for simplicity, which indeed produce discontinuity in deformation u_r. This heuristic Ansatz, however, does not qualitatively influence the results. The discontinuous deformation is obtained only in first approximation (to avoid numerical solution of Eq. (1)). In fact, in our picture the stages of one elongation period (growth) are:

1. Recovery through wall building at 'a' – interface which is a visco-plastic process (elastic equations do not apply here, because of wall and mass production; the system is merely plastic and both subdomains are weakly coupled from the mechanical point of view).
2. Production of strain and deformation on 'a' (the equations apply).
3. Production of the wall stress on both sides of 'a' – interface, and the resulting strain: visco-elastic process (equations apply).
4. Relaxation of the elastic strain in one cycle to produce elongation.
[Go to 1. to start another oscillation].

It seems, that the calculated discontinuity in deformation, even though not precisely predicted in the model, implicates, among others, burst at the transition 'a' zone (Movie S3). Note, in our model the growth (plastic extension) is also limited to this region.

Best regards,

M. Pietruszka and M. Lipowczan