  We develop a new nonlinear method to model structure formation in general
relativity from a generalization of the relativistic Lagrangian perturbation
schemes, controlled by Szekeres (and LTB) exact solutions. The overall approach
can be interpreted as the evolution of a deformation field on an inhomogeneous
reference model, obeying locally Friedmann-like equations. In the special case
of locally one-dimensional deformations, the new model contains the entire
Szekeres family of exact solutions. As thus formulated, this approach
paraphrases the Newtonian and relativistic Zel'dovich approximations, having a
large potential for applications in contexts where relativistic degrees of
freedom are relevant. Numerical simulations are implemented to illustrate the
capabilities and accuracy of the model.
