= Solution
A material fibre segment of reference length $L$ and unit direction $l$ has reference <vector> $Ll$. The uniform <deformation gradient> maps it to $LAl$, whose current length is
$$
L|Al|=L\sqrt{l^TA^TAl}.
$$
Therefore its length is preserved if and only if
$$
\boxed{l^TA^TAl=1.}
$$
This is the <inextensible fibre constraint>. The <quadratic form> uses the <right Cauchy-Green deformation tensor>; a subsequent rigid rotation does not change it, consistently with the polar factorization $A=RU$.
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