Nametchougle Dampotime¹, Kossi Atchonouglo^2,, Edo-Owodou Ayeleh³

Hooke’s Law Formula is given as , where F denotes the force applied, is the displacement extension and k is the spring constant or force constant. In classical linear elasticity, with the stress tensor σ and the strain tensor ε, the generalized Hooke's law is written: , where the tensor of fourth order is called tensor of elasticity. It is a tensor generalization of the stiffness constant k of a spring. The invariants of the elasticity tensors represent mechanical characteristics of the anisotropic materials (such as elasticity, ductility, resistance to deformations), help to classify materials following their symmetries, which generalize the concept of “stiffness of a spring”. In this paper, we perform the calculation of invariants for the anisotropic elasticity tensor under the rotation action of SO(3) groups. The tools developed by G. de Saxé et al. [1] to determine the independent invariants in 2D, essentially consisting of changing reference base and Kelvin’s decomposition of the elasticity tensor, are borrowed for the 3D case. In total, eighteen independent invariants also called global invariant emerge including 5 for the first order and thirteen for higher order. At the end, we give the physical signification of these invariants for isotropic materials.

Representation theory, Anisotropy, Linear elasticity