A new proof that the number of linear elastic symmetries is eight

It is shown here that there are exactly eight different sets of symmetry planes that are admissible for an elasticity tensor. Each set can be seen as the generator of an associated group characterizing one of the traditional symmetry classes.

[1]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .

[2]  T. C. T. Ting,et al.  Anisotropic Elasticity: Theory and Applications , 1996 .

[3]  Robert Bruce Lindsay,et al.  Physical Properties of Crystals , 1957 .

[4]  G. Piero,et al.  On the completeness of the crystallographic symmetries in the description of the symmetries of the elastic tensor , 1991 .

[5]  Stephen C. Cowin,et al.  Anisotropic Symmetries of Linear Elasticity , 1995 .

[6]  James Casey,et al.  Theoretical, Experimental, and Numerical Contributions To the Mechanics of Fluids and Solids - Foreword , 1995 .

[7]  S C Cowin,et al.  Identification of the elastic symmetry of bone and other materials. , 1989, Journal of biomechanics.

[8]  F. Fedorov Theory of Elastic Waves in Crystals , 1968 .

[9]  A. Maradudin,et al.  An Introduction To Applied Anisotropic Elasticity , 1961 .

[10]  Maurizio Vianello,et al.  Symmetry classes for elasticity tensors , 1996 .

[11]  G. F. Smith,et al.  THE STRAIN-ENERGY FUNCTION FOR ANISOTROPIC ELASTIC MATERIALS , 1958 .

[12]  On the number of distinct elastic constants associated with certain anisotropic elastic symmetries , 1995 .

[13]  Stephen C. Cowin,et al.  PROPERTIES OF THE ANISOTROPIC ELASTICITY TENSOR , 1989 .

[14]  Stephen C. Cowin,et al.  A multidimensional anisotropic strength criterion based on Kelvin modes , 2000 .

[15]  S. Cowin,et al.  On the Identification of Material Symmetry for Anisotropic Elastic Materials , 1987 .

[16]  Leopold Alexander Pars,et al.  A Treatise on Analytical Dynamics , 1981 .

[17]  M. Hayes,et al.  STATIC IMPLICATIONS OF THE EXISTENCE OF A PLANE OF SYMMETRY IN AN ANISOTROPIC ELASTIC SOLID , 1992 .

[18]  S. Forte,et al.  Functional bases for transversely isotropic and transversely hemitropic invariants of elasticity tensors , 1998 .

[19]  J. Nye Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .