In physical problems the infinite force is easily implemented by the mathematical form of that force, take $1/r$ as an example, whenever the distance between two particles becomes small the force goes to infinity. But, I want to simulate a system using agent-based modeling which the force between two objects becomes infinity without any mathematical form, my question is: Can the type of force below be implemented in a computer simulation? If so, how is it done?$$f_{ij} = \hat{r}_{ij}\begin{cases}-\infty &\text{if } r_{ij} < r_\text{hc}\\\frac{1}{4}\frac{r_{ij} - r_e}{r_a - r_\text{hc}} &\text{if } r_\text{hc}<r_{ij}<r_a\\1 &\text{if } r_a< r_{ij}<r_c \end{cases}$$This equation is from a paper which has the arxiv version.
Infinite force in simulation
simulation