A Modified Fully Implicit Cutting Plane Method Based Stress Integration Algorithm and its Verification Using Drucker Prager Model
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It is necessary to have capable elasto-plastic stress integration algorithms to simulate phenomenon involving complex plasticity models with nonlinear effects such as non-linear elastic constitutive relations, pressure dependance, and involvement of all three stress invariants in the yield criterion. A novel fully implicit elasto-plastic stress integration algorithm is proposed based on modifications made to the Cutting Plane Method (CPM). We discuss its features in comparison to the Closest Point Projection Method (CPPM) and CPM. The modifications made to CPM involve the formation of implicit equations using the incremental form representations of state variables, stress and the plastic internal variables. Furthermore, the proposed algorithm constitutes a consistent tangent operator derived in a straightforward manner similar to CPPM. We perform several numerical tests using Drucker Prager plasticity with nonlinear elastic constitutive relations and nonlinear hyperbolic isotropic hardening rules. The single material point test and iso-error surfaces reveal that the proposed algorithm provides stress remapping that are as good as CPPM, though slight disparities are observed. A strain loading history test is also performed to evaluate the performance of the consistent tangent operator which reveal that despite the nonlinear effects involved, the proposed method is as capable as CPPM in the cases considered.
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