Symmetry classes in piezoelectricity from second-order symmetries

The piezoelectricity law is a constitutive model that describes how mechanical andelectric fields are coupled within material. In its linear formulation this comprises threeconstitutive tensors of increasing order: the second order permittivity tensor S, third orderpiezoelectricity P and fourth-order elasticity C. first part paper,the symmetry classes alone investigated. Using new approachbased on use so-called clips operations, we establish 16 thistensor provide their associated normal forms. Second orthogonal transformations(plane symmetries $\pi$-angle rotations) then used to characterize classify directly 11out tensor. An additional step distinguishthe remaining proposed