= Solution
{c}
Write $\lambda=L_1/L_0>1$. The one-dimensional <multiplicative decomposition of the deformation gradient> reads $\ell/L_0=\alpha\gamma$. Before contact, $\alpha=1$; afterwards, the imposed fixed length gives
$$
\alpha(t)=\frac{\lambda}{1+ct},\qquad t\ge t_c.
$$
Substituting in the linear <constitutive equation> yields
$$
\boxed{n(t)=\begin{cases}
0,&0\le t\le t_c,\\
E_s\left(\dfrac{\lambda}{1+ct}-1\right),&t>t_c.
\end{cases}}
$$
Here negative <axial stress> means compression. The two branches agree at $t_c$ because $1+ct_c=\lambda$. At late times,
$$
\alpha\to0,\qquad n\to-E_s.
$$
Thus the law permits arbitrarily severe elastic shortening at a finite compressive <stress>. It is a small-<strain> approximation, appropriate near $\alpha=1$, and is not a credible material law as $\alpha\to0$. The one-dimensional constraint rules out <buckling> in this particular model; the finite limiting <stress> is a defect of extrapolating the linear <constitutive equation>, even with that constraint retained.
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