Projector representation of isotropic linear elastic material laws for directed surfaces
Résumé
In the framework of linear elasticity, it is possible to use eigenspace projectors to describe the elasticity tensor, at least for special cases of material symmetries. A similar procedure is also advantageous in the context of directed surfaces. It is thus possible to introduce this representation to stiffness measures of thin-walled members. Hereby, we reduce our considerations to an elastic mid-surface, where the in-plane, out-of-plane, and transverse shear states are uncoupled, but superposed eventually. Thereby, we introduce a unique decomposition of the stiffness measures for the considered deformation states, while we limit our considerations to homogeneous materials without pronounced orientation dependency. For each of these three states, eigenvalues of the stiffness tensors are evaluated based on engineering material parameters. Finally, the whole procedure allows for the clear distinction of dilatoric and deviatoric portions in the constitutive equations.
After all, a compact and mathematically easy-to-handle representation for the stiffness tensors with respect to in-plane, out-of-plane, and transverse shear state has been found. Thereby, we show correlations to classical representations as well as advantages due to the clarity of present scheme.