= Solution
{c}
The kinematic relation is unchanged: $\alpha=1$ before contact and $\alpha=\lambda/(1+ct)$ afterwards. Therefore the nonlinear <constitutive equation> gives
$$
\boxed{n(t)=\begin{cases}
0,&0\le t\le t_c,\\
E_s\left[\dfrac{\lambda^2}{(1+ct)^2}-\dfrac{1+ct}{\lambda}\right],&t>t_c.
\end{cases}}
$$
The first term in the post-contact expression is $O(t^{-2})$. Hence its <asymptotic expansion> is
$$
n(t)=-\frac{E_sc}{\lambda}t-\frac{E_s}{\lambda}+O(t^{-2}),\qquad
\boxed{n(t)\sim-\frac{E_scL_0}{L_1}t\quad(t\to\infty).}
$$
In this model the compressive <axial stress> diverges in magnitude, because the $-\alpha^{-1}$ term penalizes vanishing elastic <stretch ratio> without bound.
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