Numerical differentiation for local and global tangent operators in computational plasticity

In this paper, numerical differentiation is applied to integrate plastic co nstitutive laws and to compute the corresponding consistent tangent operato rs. The derivatives of the constitutive equations are approximated by means of difference schemes. These derivatives are needed to achieve quadratic c onvergence in the integration at Gauss-point level and in the solution of t he boundary value problem. Numerical differentiation is shown to be a simpl e, 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. (C) 2000 Elsevier Science S.A. All rights reserved.