A cylindrical sample with a $3\mathrm{.}6$ mm diameter and height of $2\mathrm{.}2$ mm of a homogeneous incompressible and isotropic neo$-$Hookean material is uniaxial stretched in the Zdirection by $1$ mm$.$ At maximum displacement a force of $9\mathrm{.}1$ kN is recorded and there is no stress relaxation. Determine the following: $($i$)$ The deformation gradient tensor. $[3$ Marks$]($ii$)$ The Cauchy strain tensor. $[3$ Marks$]($iii$)$The initial shear modulus.