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The ability of the symplectic Brezis-Ekeland-Nayroles principle has been shown in the standard plasticity where the material obeys associated flow rules. Recently, Harakeh et al. in Symplectic bipotentials [24] proposed a generalization of the SBEN principle to non-associated dissipative laws by replacing in the BEN functional the sum of the dissipation potential and its Fenchel polar by the bipotential. The aim of the present work is to demonstrate the capability of the extended version of the SBEN principle for the numerical simulation of non-associated elasto-plastic problems. We applied this approach to the thick-walled tube problem in the quasi-static case by using the Drucker-Prager model based on the bipotential. The accuracy of the SBEN principle is assessed by comparing the numerical results with those obtained by using the classical incremental finite element procedure.

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A Non-incremental Numerical Method for Non-associated Elastoplastic Problems Using the SBEN Principle and the Bipotential

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  • 发表日期：

    2026年

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  • Danial Hussain,
  • Abdelbacet Oueslati,
  • Pierre Gosselet,
  • Géry de Saxcé,
  • Djimedo Kondo

摘要

The ability of the symplectic Brezis-Ekeland-Nayroles principle has been shown in the standard plasticity where the material obeys associated flow rules. Recently, Harakeh et al. in Symplectic bipotentials [24] proposed a generalization of the SBEN principle to non-associated dissipative laws by replacing in the BEN functional the sum of the dissipation potential and its Fenchel polar by the bipotential. The aim of the present work is to demonstrate the capability of the extended version of the SBEN principle for the numerical simulation of non-associated elasto-plastic problems. We applied this approach to the thick-walled tube problem in the quasi-static case by using the Drucker-Prager model based on the bipotential. The accuracy of the SBEN principle is assessed by comparing the numerical results with those obtained by using the classical incremental finite element procedure.