Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1987 · 61 citations · 6 references
Natural SciencesMaterials SciencePhysicsBiomechanicsMechanical Behavior Of MaterialsStructural MaterialsElastic DeformationElastic PropertiesElasticity TheoryElasticityHyperelasticityMaterial Symmetry ClassesStiffness TensorSymmetry TransformationsTensor Formulation Of ElasticityTransformationsTransversely Isotropic Materials
Abstract A representation formula for the elasticity tensor of a linearly elastic, transversely isotropic material is obtained, depending on eight constants. If, besides rotations about the axis of symmetry, reflections with respect to planes through that axis are also regarded as admissible symmetry transformations for the material, it is shown that the number of constants reduces to six. It is also shown that, no matter whether reflections belong to the collection of admitted symmetry transformations or not, only five constants are needed for hyperelastic materials.
6