DEFORMATION EXTRAPOLATION AND INITIAL PREDICTORS IN LARGE-DEFORMATIONFINITE-ELEMENT ANALYSIS

In implicit Lagrangian finite element formulations, it is generally ne cessary to extrapolate to time t(k+1) the motion in the converged time step t(k-1) --> t(k), in order to provide an initial predictor for th e solution at time t(k+1). This extrapolation is typically carried out by assuming a constant material velocity field in [t(k-1), t(k+1)]. H owever, this practice can lead to a poor initial estimate of the equil ibrium solution at t(k+1), particularly when moderate or large rotatio n increments are involved. In some cases, the constant-material-veloci ty-field extrapolation is so inaccurate that convergence of the subseq uent equilibrium iteration is precluded. The proposed technique involv es extrapolation of the stretch and rotation fields rather than the di splacement field. The extrapolated stretch and rotation are used to re compose a local deformation gradient which is, in general, incompatibl e. However, a compatible deformation field is recovered by minimizatio n of a suitably-defined quadratic functional. This constrained minimiz ation problem determines the displacement field that is closest, in a certain sense, to the extrapolated stretch and rotation. In this manne r, an initial predictor is determined that is much more accurate, in m any situations, than that given by the simple constant-nodal-velocity assumption. Three numerical examples are presented that illustrate the effectiveness of the proposed extrapolation method.