HUESPE Alfredo Edmundo
On the numerical resolution of the discontinuous material bifurcation problem
J. OLIVER; A. E. HUESPE; J. C. CANTE; G. DIAZ
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
JOHN WILEY & SONS LTD
Año: 2010 vol. 83 p. 786 - 804
The work focuses on the numerical resolution of the discontinuous material bifurcation problem as arelevant ingredient in computational material failure mechanics. The problem consists of finding theconditions for the strain localization onset in terms of the so-called bifurcation time, localization directionsand localization modes. A numerical algorithm, based on the iterative resolution of a coupled eigenvalueproblem in terms of the localization tensor, is proposed for such purpose. The algorithm is shown tobe always convergent to the exact solution for the symmetric case (major and minor symmetries ofthe tangent constitutive operator). In the unsymmetric case (only minor symmetries), the solution is nolonger exact, although it is shown that using the symmetric part of the localization tensor in the proposedalgorithms provides enough accurate solutions for most of cases. Numerical examples illustrate the benefitsof the proposed methodology in terms of accuracy and savings in the computational cost associated withthe problem.