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In a previous paper, we proposed a symplectic version of the Brezis-Ekeland-Nayroles principle. We applied it to the standard plasticity. The object of this work is to extend the previous formalism to non associated laws. For this aim, we introduce the concept of symplectic bipotential which extends that of bipotential to dynamical systems. We present a method to build it from a bipotential. Next, we generalize the symplectic Brezis-Ekeland-Nayroles principle to the non associated dissipative laws. As example, we apply it to the unilateral contact law with Coulomb’s dry friction.

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Symplectic Bipotentials for the Dynamics of Dissipative Systems with Non Associated Constitutive Laws

  • 会议论文

  • 发表日期：

    2026年

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  • Mohamad Harakeh,
  • Michael Ban,
  • Géry de Saxcé

摘要

In a previous paper, we proposed a symplectic version of the Brezis-Ekeland-Nayroles principle. We applied it to the standard plasticity. The object of this work is to extend the previous formalism to non associated laws. For this aim, we introduce the concept of symplectic bipotential which extends that of bipotential to dynamical systems. We present a method to build it from a bipotential. Next, we generalize the symplectic Brezis-Ekeland-Nayroles principle to the non associated dissipative laws. As example, we apply it to the unilateral contact law with Coulomb’s dry friction.