Some new properties of the Eshelby stress tensor

Erwan Verron (1) , Malik Aït-Bachir (1) , Philippe Castaing (2)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 CEntre Technique des Industries Mécaniques - Cetim (FRANCE)

The Eshelby stress tensor is known to be an appropriate Continuum Mechanics quantity to capture singularities. Nevertheless, even if its use in the calculation of configurational forces is well-established, its peculiar properties were investigated only recently. Here, some new properties of this tensor are studied. In this way, it is assumed that the evolution of microscopic defects in the material can be predicted at the macroscopic scale by examining the components of the Eshelby stress tensor. More precisely, considering that defects can be modeled by material surfaces oriented in all possible directions and assuming that they are able to evolve in every possible directions, it is shown that the maximum amount of energy which can be released by defects evolution is partially contained in the tensor. In the special case of hyperelasticity, the corresponding optimization problem is established and solved for both isotropic and anisotropic materials.

Domaines: Mécanique [physics.med-ph]; Matériaux

Erwan Verron, Malik Aït-Bachir, Philippe Castaing. Some new properties of the Eshelby stress tensor. IUTAM Symposium. Progress in the theory and numerics of Configurational Mechanics, 2008, Erlangen-Nuremberg, Germany. ⟨10.1007/978-90-481-3447-2_3⟩. ⟨hal-01008936⟩