Computational field of solid mechanics is mostly dominated by FEM.   This is a well known topic.

But is it that  FDM (finite difference method) has no chance of surviving
in solid mechanics?

What are the present developments in the use of FDM in case of elasticity analysis of solid body?

I would like to mention some of the recent research works on this topic here.....

Recently a new mathematical model has been developed by Prof. S. Reaz Ahmed and his students known as the "displacement potential approach".