A displacement-like finite element model for \(J_2\) elastoplasticity: Variational formulation and finite-step solution. (English) Zbl 0964.74061
Summary: We revisit the displacement-like finite element formulation for finite-step \(J_2\) elastoplasticity. The classical computational strategy, according to which plastic loading is tested at Gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements, is consistently derived from a suitably discretized version of a min-max variational principle. The sequence of solution phases to be performed within each load step adopting a full Newton’s method is illustrated in detail, and the importance of a correct update of the plastic strains is emphasized. Next we show that, in order to increase the rate of convergence and the stability properties of the Newton’s method, the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of structural model. This is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step. The effectiveness of the present approach is shown by a set of numerial examples referred to plane strain problems.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
Keywords:
J(2)-elastoplasticity; Gauss points; return mapping algorithm; min-max variational principle; Newton’s method; convergence; stability; elastoplastic tangent operator; load step; plane strainReferences:
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