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?


Google for the “Forward Increment Lagrange Multiplier Method” of Carpenter et al. [1991].

For implementation, see the code here (especially lines 463-497 in src/main.F90).

If you also have friction then see the modified version here (implementation here (deprecated) and here).

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    $\begingroup$ You should add more detail into how the method works within the context of the codes that you linked to. $\endgroup$ – Paul Jun 7 '17 at 19:33

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