Elastic stiffness tensor

In many cases considerable simplification is possible, because of the constraints imposed on the number of independent elastic constants. For cubic symmetry, for which the elastic stiffness tensor has only three independent constants as given in (6.29), the elements of T, are given in Table 11.1(b), and for hexagonal symmetry the elements are given in Table 11.1(c). If c12 = Cn - 2c44 were to be substituted in Table 11.1(b) the isotropic elements would... 

If the solid is linear elastic (stiffness tensor C = S,v ), the potential energy Fj 1 takes the form (Deude et al., 2002) ... 

These simplifications reduce the size of the elasticity tensors from [9 x 9] to [6 x 6], with 36 elastic coefficients. The shorthand notation normally used for the elasticity tensors are now introduced, namely, that the subscripts become 1 11 2 22 3 33 4 23, 32 5 31, 13 and 6 12, 21. With this change, the elastic stiffness tensor may be written in matrix form as ... 

Draw, in matrix notation, the elastic-stiffness tensor for a tetragonal monocrystal in the 422 class. 

The effective elastic stiffness tensor of damaged material C(d) is given by ... 

Coefficients aij T) depend explicitly on temperature T. Coefficients afj, aijki, are supposed to be temperature independent, constants giju and Vijkimn determine the magnitude of the gradient energy. Tensors gijki, Oijki and positively defined. Tensor is the surface excess elastic moduli, p, p is the surface stress tensor [81,82], is the surface piezoelectric or piezomagnetic tensor [67], qijki are the bulk striction coefficients Ciju are components of elastic stiffness tensor [83]. 

Here My are strain tensor components, Ciju are components of elastic stiffness tensor. 

X10. The next three rows present the viscosity rj, the surface tension, and its tenqterature dependence, in the liquid state. The next properties are the coefficient of linear thermal expansion a and the sound velocity, both in the solid and in the liquid state. A number of quantities are tabulated for the presentation of the elastic properties. For isotropic materials, we list the volume compressihility k = —(l/V)(dV/dP), and in some cases also its reciprocal value, the bulk modulus (or compression modulus) the elastic modulus (or Young s modulus) E the shear modulus G and the Poisson number (or Poisson s ratio) fj,. Hooke s law, which expresses the linear relation between the strain s and the stress a in terms of Young s modulus, reads a = Ee. For monocrystalline materials, the components of the elastic compliance tensor s and the components of the elastic stiffness tensor c are given. The elastic compliance tensor s and the elastic stiffness tensor c are both defined by the generalized forms of Hooke s law, a = ce and e = sa. At the end of the list, the tensile strength, the Vickers hardness, and the Mohs hardness are given for some elements. 

General Static dielectric constant Dissipation factor Elastic stiffness tensor Elastic compliance tensor Elastooptic tensor... 

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