Loss of stability, bifurcation and branch switching are three important
issues in the numerical modeling of soil. The homogeneous deformation
of soil can be modeled quite well in contrast to the regime beyond
homogeneous deformations, i.e.\ that of localized deformations.
The transition from homogeneous to localized deformation is frequently
characterized by a bifurcation point, indicating loss of uniqueness of the
solution.
A bifurcation point in the solution path is often (and in typically so in the
examples considered here) a consequence of spatial symmetry and
of the homogeneous distribution of
material parameters. At a certain load level, there may be more
than one possible solution but most paths will be unstable.
Material perturbation is a generally accepted method to circumvent the
problem of loss of uniqueness. This however, may influence the peak load
and the shape of the post-bifurcation deformation.
Eigenvectors related to negative eigenvalues can be used to perturb an
unstable state and to arrive at a stable path. This procedure is called branch
switching. Moreover, the signalling of bifurcation via the eigenvalues of
the structural matrix is reconsidered and related to stability.