ISSN:
0029-5981
Keywords:
Gurson model
;
numerical algorithms
;
consistent tangent moduli
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
We investigate the generalized mid-point algorithms for the integration of elastoplastic constitutive equations for the pressure-dependent Gurson-Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric parts, a formula for explicitly calculating the consistent tangent moduli with the generalized mid-point algorithms is derived for the Gurson-Tvergaard model. The generalized mid-point algorithms, together with the consistent tangent moduli, have been implemented into ABAQUS via the user material subroutine. An analytical solution of the Gurson-Tvergaard model for the plane strain tension case is given and the performances of the generalized mid-point algorithms have been assessed for plane strain tension and hydrostatic tension problems and compared with the exact solutions. We find that, in the two problems considered, the generalized mid-point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid-point algorithm (α = 0·5) the most accurate one. Considering the extra non-symmetrical property of the consistent tangent moduli of the algorithms with α 〈 1, the Euler backward algorithm (α = 1) is, perhaps, the best choice.
Additional Material:
7 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620381206
