Consider simple tension and shear tests, and use the relationship among $G($shear modulus$),$ E $($Young$\text{'}$s Modulus$)$ and v $($Poisson$\text{'}$s ratio$)$ for isotropic materials to show the equation set $($A$)$ follow from Equation set $($B$).$

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${}_{11},=(+2G){}_{11}+{}_{22}+{}_{33}$

$,{}_{22}={}_{11}+(+2G){}_{22}+{}_{33}$

$,{}_{33}=([{}_{11}+{}_{22}+(+2G){}_{33})=(1,2$;$1,3$;$2,3])=C_{11}{}_{11}+C_{12}{}_{22}++C_{12}{}_{33}$

${}_{22}=C_{12}{}_{11}+C_{111}{}_{22}++C_{12}{}_{33}$

${}_{33}=([C_{12}{}_{11}+C_{12}{}_{22}++C_{11}{}_{33}$

Note: $,=\frac{Ev}{(1+v)(1-2v)}$