Numerical differentiation for local and global tangent operators in computational plasticity

Author (s): Pérez-Foguet, A., Rodríguez-Ferran, A. and Huerta, A.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 189, Issue 1
Pages: 277 – 296
Date: 2000


In this paper, numerical differentiation is applied to integrate plastic constitutive
laws and to compute the corresponding consistent tangent operators. The derivatives
of the constitutive equations are approximated by means of difference schemes.
These derivatives are needed to achieve quadratic convergence in the integration
at Gauss-point level and in the solution of the boundary value problem. Numerical
differentiation is shown to be a simple, robust and competitive alternative to
analytical derivatives. Quadratic convergence is maintained, provided that adequate
schemes and stepsizes are chosen. This point is illustrated by means of some numerical



@article {2000-CMAME-PRH,
author = {{P}/'erez-{F}oguet, {A}gust/'i and {R}odr/'iguez-{F}erran, {A}ntonio and {H}uerta, {A}ntonio},
title = {{N}umerical differentiation for non-trivial consistent tangent matrices: an application to the {MRS}-Lade model},
journal = {{I}nternational {J}ournal for {N}umerical {M}ethods in {E}ngineering},
volume = {48},
number = {2},
doi = {10.1002/(SICI)1097-0207(20000520)48:2<159::AID-NME871>3.0.CO;2-Y},
pages = {159--184},
year = {2000},