Bending stress of beam in contact with a flat surface?

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I am designing a spinal disc with 2 metal endplates. These endplates are rectangular in shape and are fixed to form a flat contact surface with the vertebrae bone surface.

My question is based on the bending stress of these metal endplates. I need to work out the possible thickness of these endplates. I understand how a beam can be modelled with simple supports, cantilever etc but in this case the endplate is flat pressed against a flat surface so contact is over the whole surface area and it is to support a compressive force in the centre of the endplate length L.

Please could anyone offer me suggestions as to how i could calculate this?
 

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