Formulation of implicit finite element methods for multiplicative finite deformation plasticity
Some constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non-symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near-incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.
© 1990 John Wiley & Sons. Received 22 November 1988. Revised 11 June 1989. The support of the NSF Materials Research Group is gratefully acknowledged. The computations reported in this paper were performed on the Alliant FX8 of the Computational Mechanics Facility of the Division of Engineering at Brown University. The acquisition of this computer was made possible, in part, by grants from the US National Science Foundation and the Office of Naval Research.