An alternative to the Kelvin decomposition for plane anisotropic elasticity

Boris Desmorat (1) , Paolo Vannucci (2)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 LMV - Laboratoire de Mathématiques de Versailles

In this paper we propose an alternative tensorial decomposition to the Kelvin's one (introduced by Kelvin in 1856) for plane anisotropic elasticity using the polar formalism (introduced by Verchery in 1979). In a first part of the paper, a parallel between the two approaches is proposed. Thanks to it, some new results are found ; namely, the projectors introduced have a direct interpretation in terms of material symmetry and are intrinsic for any type of symmetry considered, i.e. they do not depend on any elastic modulus for any type of symmetry, unlike in the Kelvin decomposition. The introduction of what we call, in the paper, the polar projectors, stresses and strains gives a new insight into the polar formalism. The results proposed in this paper will hopefully be useful in some cases, for example in the modeling of anisotropic damage evolution in solids.

Mots clés: Kelvin decomposition; Anisotropy; Polar formalism; Elastic invariants

Domaines: Mécanique [physics]

Boris Desmorat, Paolo Vannucci. An alternative to the Kelvin decomposition for plane anisotropic elasticity. Mathematical Methods in the Applied Sciences, 2013, pp.10.1002/mma.3059. ⟨10.1002/mma.3059⟩. ⟨hal-00947892⟩