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Abstract

Two algorithms for the stress update (ie time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unified derivation of both algorithms in spite of their inherent differences. Then the two algorithms are adapted from convected frames to a fixed Cartesian frame and implemented in a small-strain finite element code. The implementation is validated be means of a set of simple deformation paths and two benchmark tests in non-linear mechanics. In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis.

Additional information

Authors: RODRIGUEZ-FERRAN A, Universitat Politècnica de Catalunya, Departamento de Matemática Aplicada, Barcelona (ES);HUERTA A, Universitat Politècnica de Catalunya, Departamento de Matemática Aplicada, Barcelona (ES);PEGON P, JRC Ispra (IT)
Bibliographic Reference: Article: International Journal for Numerical Methods in Engineering, Vol. 40 (1997), pp. 4363-4404
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