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

Abstract:
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 examples.

     



Bibtex:
	@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},
}