IMPLICIT INTEGRATION OF ELASTOPLASTIC CONSTITUTIVE MODELS FOR FRICTIONAL MATERIALS WITH HIGHLY NONLINEAR HARDENING FUNCTIONS

Constitutive relations in elastoplasticity may be formulated in a vari ety of ways, and different update algorithms may be employed to solve the resulting equations. Several implicit integration schemes, althoug h some not widely used, have been suggested in the last years. Among t hem, the closest point projection method (CPPM) has proven to be an ef fective and robust integration scheme. In order to gain maximum contro l of the stress projection, a two-level CPPM iteration scheme is propo sed. The hardening variables are fixed during the stress projection on to consequently fixed yield surfaces, and after the stress projection, new values of the hardening variables are calculated defining new yie ld surfaces. The update of the hardening parameters which, in general, may be highly nonlinear functions, may be determined by a combination of a Picard Iteration (PI) on the hardening variables and an adaptati ve order inverse interpolation (AOII) on the difference of subsequent iterations of the hardening variables. The integration scheme has been implemented in a general constitutive driver which has been formulate d independent of the selected constitutive model and easily linked to finite element codes. A third stress invariant dependent, cone-cap ela stoplastic constitutive model, referred to as the MRS-Lade, with a hig hly non-linear hardening function has been used to show the applicabil ity of the proposed iteration scheme. Error analyses and accuracy asse ssment are presented along with some representative test results. (C) 1997 by John Wiley & Sons, Ltd.