Numerical differentiation for local and global tangent operators in computational plasticity
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In this paper, numerical di¿erentiation 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 di¿erence 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 di¿erentiation 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.
CitationPérez-Foguet, A.; Rodriguez, A.; Huerta, A. Numerical differentiation for local and global tangent operators in computational plasticity. "Computer methods in applied mechanics and engineering", 2000, vol. 189, p. 277-296.