An alternative to the Kelvin decomposition for plane anisotropic elasticity

Abstract

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 the 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, that is, 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. Copyright © 2013 John Wiley & Sons, Ltd.