$2\mathrm{.}19.$ A $3-$m by $1-$m by $2-$m parallelepiped is deformed by movement of comer $A$ to $,$

$1\mathrm{.}0003,1\mathrm{.}9994),$ as shown in Fig. P$2\mathrm{.}19.$ Assuming that the displacement field is given by Eqs.

$(2\mathrm{.}22),$ calculate at point $A($a$)$ the strain components and ascertain whether this strain distribution is

possible; $($b$)$ the normal strain in the direction of line $AB$; and $($c$)$ the shearing strain for the

perpendicular lines $AB$ and $AC.$

Answers

a$.\left[\begin{array}{ccc}-167& -200& -225\\ -200& 300& -225\\ -225& -225& -300\end{array}\right]$

b$.-416$ microns

c$.-582$ microns