A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations
By assuming from the outset hyperelastic constitutive behavior, an alternative approach to finite deformation plasticity and viscoplasticity is proposed whereby the need for integration of spatial rate constitutive equations is entirely bypassed. To enhance the applicability of the method, reference is made to a general formulation of plasticity and viscoplasticity which embodies both the multiplicative and additive theories. A new return mapping algorithm capable of accommodating general yield conditions, arbitrary flow and hardening rules and non-constant tangent elasticities is proposed. Finally, a numerical example is presented which illustrates the excellent performance of the method for very large time steps.
© 1985 Elsevier. Revised manuscript received 12 September 1984. We wish to thank Profs. Jerrold E. Marsden, Karl. S. Pister and Robert L. Taylor for many helpful discussions.