On the Formulation of Closest-Point Projection Algorithms in Elastoplasticity. Part II: Globally Convergent Schemes. With applications to deviatoric and pressure-dependent plastic models.

Author (s): Pérez-Foguet, A. and Armero, F.
Journal: International Journal for Numerical Methods in Engineering

Volume: 53, Issue 2
Pages: 331 – 374
Date: 2002


This paper presents the formulation of numerical algorithms for the solution of
the closest-point projection equations that appear in typical implementations
of return mapping algorithms in elastoplasticity. The main motivation behind this
work is to avoid the poor global convergence properties of a straight application
of a Newton scheme in the solution of these equations, the so-called Newton-CCPM.
The mathematical structure behind the closest-point projection equations identified
in Part I of this work delineates clearly different strategies for the successful
solution of these equations. In particular, primal and dual closest-point projection
algorithms are proposed, in non-augmented and augmented Lagrangian versions for
the imposition of the consistency condition. The primal algorithms involve a direct
solution of the original closest-point projection equations, whereas the dual
schemes involve a two level structure by which the original system of equations
is staggered, with the imposition of the consistency condition driving alone the
iterative process. Newton schemes in combination with appropriate line search
strategies are considered, resulting in the desired asymptotically quadratic local
rate of convergence and the sought global convergence character of the iterative
schemes. These properties, together with the computational performance of the
different schemes, are evaluated through representative numerical examples involving
different models of finite strain plasticity. In particular, the avoidance of
the large regions of no convergence in the trial state observed in the standard
Newton-CPPM is clearly illustrated.



@article {2002-IJNME-PA,
author = {P\'erez-Foguet, A. and Armero, F.},
title = {On the formulation of closest-point projection algorithms in elastoplasticity—part II: Globally convergent schemes},
journal = {International Journal for Numerical Methods in Engineering},
volume = {53},
number = {2},
pages = {331--374},
doi = {10.1002/nme.279},
issn = {1097-0207},
year = {2002},