Operator split methods for the numerical solution of the elastoplastic dynamic problem

Abstract

The elastoplastic dynamic problem is first formulated in a form that facilitates the application of product formula techniques. The additive decomposition of the dynamic equations into elastic and plastic parts is taken as a basis for the definition of product algorithms that exploit such decomposition. In the context of a finite element discretization, these product algorithms entail, for every time step, the solution of an elastic 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 relations. 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 product algorithm are identical to those of the elastic algorithm used whereas the computational expense is practically equal to that of an elastic problem.

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