Anisotropic Materials Contracted Notation

In an anisotropic material, coupling can exist between all stresses and all strains. Hence, the generalized Hooke s law for a linearly elastic anisotropic material, expressed using matrix algebra, has no zeros appearing in the compliance matrix  

This expression can be written in Cartesian tensor notation and matrix notation, respectively, as 

Contracted notation EN, Engineering notation TN, Tensor notation. 

Contracted notation (CN) has been introduced in the equations, where it is convenient for computer solution to use single-digit subscripts to designate stress and strain terms. The relationships between (1) tensor or elasticity notation, (2) engineering notation (EN), and (3) CN are defined in Table 8.3. 

For an anisotropic lamina under plane stress. Equation 8.39 reduces to 

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