Tensor elasticity

Temporary deformation, 89 Tensor, elasticity, 12 strain, 11 stress, 11... 

Unlike stress and strain, which are field tensors, elasticity is a matter tensor. It is subject to Neumann s principle. Hence, the number of independent elastic coefficients is further reduced by the crystal symmetry. The proof is beyond the scope of this book (the interested reader is referred to Nye, 1957), here the results will merely be presented. For example, even with triclinic crystals, the lowest symmetry class, there are only 21 independent elastic-stiffness coefficients ... 

Symmetry point group Dielectric tensor Elastic tensor ors , Piezoelectric tensor dimn Elasto-optic tensor Pmn Electrooptic tensor rmk Nonlinear susceptibility tensors x > 1 X< > Table number... 

Static dielectric constant Dissipation factor Elastic stifbiess tensor Elastic compliance tensor Elastooptic 1 tensor ... 

General Static dielectric tensor Elastic stiffness tensor Elastooptic tensor... 

Deviatoric stress tensor Norm of deviatoric stress Lode s angle for stress Second invariant of deviatoric stress Third invariant of deviatoric stress Strain increment tensor Elastic strain increment tensor Plastic strain increment tensor Volumetric plastic strain increment tensor... 

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