Past exam of the mathematical mechanical biology course of the University of Oxford / 2023 / 3 / a / iii

The kinematic relation is unchanged: $\alpha =1$ before contact and $\alpha =\lambda /(1+ct)$ afterwards. Therefore the nonlinear constitutive equation givesThe first term in the post-contact expression is $O(t^{-2})$. Hence its asymptotic expansion isIn this model the compressive axial stress diverges in magnitude, because the $-{\alpha }^{-1}$ term penalizes vanishing elastic stretch ratio without bound.