Generally, when I model a rigid plate (for highways or hard surface) I use null material Poisson ratio of 0.3, a Young Modulus of 200 GPa , and a density of 6000 kg/m3
You can just define a rigid body (without any elastic property) in most available FEM packages (commercial and open-source).
A rigid body in Mechanical APDL (ANSYS) consists of a set of target nodes called rigid body nodes and a single pilot node. The associated target elements use the same real constant ID. The motion of the rigid body is governed by the degrees of freedom (DOFs) at the pilot node, allowing accurate representation of the geometry, mass, and rotary inertia of the rigid body.
Apart from that you should concentrate on mass and inertia properties while defining rigid body.
You can use contact elements for a rigid and deformable body. But this is a more difficult task. More simply - to set the properties of a rigid body an order of magnitude greater than the properties of deformable bodies in your task.
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