In Real Life (tm) there are no Rigid Bodies (tm), and to first order (i.e. under low strain {*}) all solids act as a springs. The rule you are looking for is Hooke's Law:
$$ F = -k \Delta x .$$
Of course, that leaves the matter of choosing the right spring constants (and noting that everything doesn't ring for ever) the right damping as well.
You're almost certainly better figuring out how to treat compound bodies and single units than trying to do a finite element analysis (even drastically simplified) at every step.
{*} Note that materials life clay which deform easily are only under low strain for exceedingly small pressures, so this rule does not apply to them in a practical sense even if it is arguably good in the low strain limit.