On the conditions for the existence of a plane of symmetry for anisotropic elastic material

Symmetry classes for elasticity tensors

“…As further examples of modern literature in which the correct idea that there are indeed eight types of anisotropic linear (hyper)elastic materials is present, albeit without any reference to a completeness proof, we would like to cite recent papers by Sutcliffe [46], Rychlewski [37] and Jadc [23]. On the other hand, three important papers by Zheng and Spencer [52], Zheng [50], and Zheng and Boehler [51 ] contain a reference to Huo and Del Piero's proof of completeness and suggest a possible alternative.…”

On the Determination of Plane and Axial Symmetries in Linear Elasticity and Piezo-Electricity

“…Note, however that the second condition is not very constructive as it requires to check all unit vectors τ τ τ perpendicular to ν ν ν. This drawback is also present in the equivalent forms used by Jaric [12] and in the generalized Cowin-Mehrabadi theorems [22]. In the present paper, we provide a positive answer to question Q for elasticity tensors, piezoelectricity tensors and totaly symmetric tensors of order 3 up to 6.…”

Optimal determination of the material symmetry axes and associated elasticity tensor from ultrasonic velocity data

“…It was shown that each of the ten distinct elastic symmetries can be characterized uniquely by the number and orientation of the planes of symmetry it possesses. So equivalent sets of necessary and sufficient conditions [6][7][8][9] upon the components of the fourth-rank modulus tensor for a given direction to be normal to a plane of symmetry were established. From a physical point of view, these directions must be both a specific axis 7 and a specific direction.…”