# Newbie help on FEM contact problem

I am modelling the time-evolution of a soft material with a tetrahedral mesh. I use an FEM method to compute the forces on each node, and then numerically integrate the positions and velocity of the nodes over time. The basic equation is

$$MU^{\prime\prime} + C^{\prime\prime} + F(U) = R$$

where $M$ and $C$ are the mass and damping matrices.

I now need to add constraints to prevent penetration with other objects and also friction.

I can’t see the connection between my current approach and the various “contact” methods I have seen in books, papers etc. I think I need to add Lagrangian terms to deal with the inequality constraint, but am getting lost in the literature.

Can anyone suggest an introductory book or paper that can help me get started?