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Hybrid free energy approach for nearly incompressible behaviors at finite strain

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Abstract

We explore the formulation of nearly incompressible behaviors at finite strain in the context of a hybrid or a mixed energy. Such an energy is a function of both an isochoric deformation and a pressure-like quantity that can be considered as an internal variable. From thermodynamical and physical considerations, new energy functions are developed to correctly describe both nearly incompressible elasticity and thermoelastic behaviors. We discuss the advantages of such a formulation; in particular, we show that this approach makes it possible to unify the variational and the thermodynamical formulations in the nearly incompressible context without using Lagrange multipliers or other specific variational principles.

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Correspondence to Stéphane Lejeunes.

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Communicated by Johlitz, Laiarinandrasana and Marco.

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Lejeunes, S., Eyheramendy, D. Hybrid free energy approach for nearly incompressible behaviors at finite strain. Continuum Mech. Thermodyn. 32, 387–401 (2020). https://doi.org/10.1007/s00161-018-0680-4

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Keywords

  • Thermomechanical coupling
  • Entropic elasticity
  • Free energy
  • Volumetric behavior