The average conformation tensor of interatomic bonds as an alternative state variable to the strain tensor: definition and first application – the case of elasticity

Thierry Désoyer (1, 2)

1 ECM - École Centrale de Marseille
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper is a first attempt to formulate an elasticity model without any strain tensor. The new state variable introduced is the average conformation tensor of interatomic bonds. This variable is built from an elementary one – the conformation tensor of the interatomic bond linking two atoms of a pure substance –, firstly in the discrete case, then in the continuous case. In each of those cases, an average internal forces tensor is defined as the derivative of a free energy density, depending only on the new variable ; in the continuous case, the generic form of the Cauchy stress tensor is deduced. Assuming an elastic behavior, and following a thermodynamic approach, an expression for the material derivative of the new variable is also given. The average conformation tensor and a strain tensor are finally connected in the case of pure tension, from what an expression for the free energy density is inferred.

Mots clés: Interatomic bonds; Conformation tensor; Continuum Mechanics; Cauchy stress tensor; Continuum Thermodynamics; Uniaxial tension; Elasticity model; Solid state

Domaines: Mécanique des matériaux [physics.class-ph]

Thierry Désoyer. The average conformation tensor of interatomic bonds as an alternative state variable to the strain tensor: definition and first application – the case of elasticity. 2017. ⟨hal-01654624v1⟩