ON A MIXED APPROACH TO THE FINITE-ELEMENT SOLUTION OF LARGE-STRAIN ELASTOPLASTIC PROBLEMS

A mixed approach to large strain elastoplastic problems is presented i n a somewhat different may to that usually used within the context of the additive split of the rate of deformation tensor into an elastic a nd plastic part. A nonlinear extended mixed variational equation, in w hich the Jacobian of the deformation gradient and the pressure part of the stress tensor appear as additional independent variables, is intr oduced. This equation is then linearized in the accordance with the Ne wton-Raphson method to obtain the system of linear equations which rep resent the basis of the mixed finite element procedure. For the case o f a bilinear isoparametric interpolation of the displacement field, an d for piece-wise constant pressure and Jacobian, simplified expression s, differing from similar expressions corresponding to mixed finite el ement implementations, are obtained. The effectiveness of the proposed mixed approach is demonstrated by means of two examples.