There is a need to develop our understanding of fully plastic contact between spheres and a flat surfaces that results in the spheres heavily deforming and eventually flattening out. Most work conducted in this area has been for relatively lightly loaded spherical contacts that deform elastically and elasto-plastically. The case considered here is also the reverse case of a rigid spherical indenter penetrating a deformable surface. The work builds on past theoretical models that used volume conservation to consider plastic deformation. The results provide relationships which may be used to model large deformations of flattened or compressed spheres. The results also show that the area of contact can be much larger than the popular geometrical truncation model for fully plastic contact between spheres and flat surfaces.

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