A CLASS OF GENERALIZED MIDPOINT ALGORITHMS FOR THE GURSON-TVERGAARD MATERIAL MODEL

We investigate the generalized mid-point algorithms for the integratio n of elastoplastic constitutive equations for the pressure-dependent G urson-Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric part s, a formula for explicitly calculating the consistent tangent moduli with the generalized mid-point algorithms is derived for the Gurson-Tv ergaard 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-Tvergaa rd model for the plane strain tension case is given and the performanc es of the generalized mid-point algorithms have been assessed for plan e strain tension and hydrostatic tension problems and compared with th e exact solutions. We find that, in the two problems considered, the g eneralized mid-point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid-poi nt algorithm (alpha = 0.5) the most accurate one. Considering the extr a non-symmetrical property of the consistent tangent moduli of the alg orithms with alpha < 1, the Euler backward algorithm (alpha = 1) is, p erhaps, the best choice.