The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is
$
\left\{\begin{array}{l}
\varepsilon_{x x} \\
\varepsilon_{y y} \\
\varepsilon_{z} \\
\gamma_{y z} \\
\gamma_{x z} \\
\gamma_{x y}
\end{array}\right\}=\left[\begin{array}{llllll}
A & C & C & 0 & 0 & 0 \\
C & A & C & 0 & 0 & 0 \\
C & C & A & 0 & 0 & 0 \\
0 & 0 & 0 & B & 0 & 0 \\
0 & 0 & 0 & 0 & B & 0 \\
0 & 0 & 0 & 0 & 0 & B
\end{array}\right]\left\{\begin{array}{l}
\sigma_{x x} \\
\sigma_{y y} \\
\sigma_{=}^{-} \\
\tau_{y z} \\
\tau_{x z} \\
\tau_{x y}
\end{array}\right\}
$
$A, B$ and $C$ are compliances which depend on the elastic properties of the material.
Which one of the following is correct?
(A)$C=\frac{A}{2}-B$
(B) $\quad C=\frac{A}{2}+B$
(C) $\quad C=A+\frac{B}{2}$
(D) $\quad C=A-\frac{B}{2}$

Question ID - 155395 | SaraNextGen Top Answer

The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is
$
\left\{\begin{array}{l}
\varepsilon_{x x} \\
\varepsilon_{y y} \\
\varepsilon_{z} \\
\gamma_{y z} \\
\gamma_{x z} \\
\gamma_{x y}
\end{array}\right\}=\left[\begin{array}{llllll}
A & C & C & 0 & 0 & 0 \\
C & A & C & 0 & 0 & 0 \\
C & C & A & 0 & 0 & 0 \\
0 & 0 & 0 & B & 0 & 0 \\
0 & 0 & 0 & 0 & B & 0 \\
0 & 0 & 0 & 0 & 0 & B
\end{array}\right]\left\{\begin{array}{l}
\sigma_{x x} \\
\sigma_{y y} \\
\sigma_{=}^{-} \\
\tau_{y z} \\
\tau_{x z} \\
\tau_{x y}
\end{array}\right\}
$
$A, B$ and $C$ are compliances which depend on the elastic properties of the material.
Which one of the following is correct?
(A)$C=\frac{A}{2}-B$
(B) $\quad C=\frac{A}{2}+B$
(C) $\quad C=A+\frac{B}{2}$
(D) $\quad C=A-\frac{B}{2}$