Linearization and return mapping algorithms for elastoplasticity models

The return mapping algorithm is one of the most e cient procedures to solve elasto-plastic problems. However, a criticism that may be lodged against this method is the di culty of the practical computation of the consistent tangent matrix when the return is non-radial. Much research has been done to handle this matrix. In this paper, a uni ed approach is presented in such a way that a simple closed-form expression gives the consistent tangent matrix for the classical constitutive relations (von Mises, Tresca, Mohr–Coulomb, Drucker–Prager). The basic ideas are in the properties of eikonal equations appearing in several elds as image treatment, short time computation in elastic waves and others. The same kinds of ideas can be extended to non-classical models