| Abstract: | 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. |
