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Published 1983 | metadata_only
Journal Article

Operator split methods in the numerical solution of the finite deformation elastoplastic dynamic problem


The spatial formulation of the elastoplastic dynamic problem for finite deformations is considered. A thermodynamic argument leads to an additive decomposition of the spatial rate of deformation tensor and allows an operator split of the evolutionary equations of the problem into "elastic" and "plastic" parts. This operator split is taken as the basis for the definition of a global product algorithm. In the context of finite element discretization the product algorithm entails, for every time step, the solution of a nonlinear elastodynamic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive equations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stability properties of the global product algorithm are shown to be identical to those of the algorithm used for the integration of the nonlinear elastodynamic problem. Numerical examples illustrate the accuracy of the method.

Additional Information

© 1983 Elsevier. Received 1 April 1982. Revised manuscript received 18 February 1983.

Additional details

August 19, 2023
August 19, 2023