An Efficient Solution Algorithm in Computational Elastoplasticity

In this analysis three-dimensional elastoplasticity boundary value problems are discussed, and an exact closed form solution is applied for the local constitutive elastoplasticity problem. In the present analysis small strain elastoplasticity problems are considered and nonlinear kinematic hardening rules are adopted for modelling the behavior of ductile materials. In the literature notable proposals for an exact closed form solution of elastoplasticity problems have been presented. However, such analyses are often restricted to plane stress problems and elastoplasticity problems with linear kinematic hardening rules. Conversely, the present approach has the capability to be suitably applied to three-dimensional inelastic problems with nonlinear kinematic hardening rules. The present procedure reduces the local constitutive equation to the solution of a single variable algebraic equation. The analytical solution of the algebraic equation can be found in exact closed form. With the present approach no iterative solution method is needed to solve the local constitutive equations of three-dimensional problems in elastoplasticity since the constitutive problem in elastoplasticity is solved in exact closed form. In the algorithmic strategy a procedure is discussed which can be suitably applied for three-dimensional elastoplastic problems. A consistent tangent operator is applied which is derived consistently with the presented numerical algorithm. The present approach is well suited to be applied also to cyclic plasticity problems.