Frictionless indentation of dissimilar elastic–plastic spheres

A ®nite element study is performed on the frictionless normal contact of elastic±plastic spheres and rigid spheres. The e€ects of elasticity, strain hardening rate, relative size of the spheres and their relative yield strength are explored. Indentation maps are constructed, taking as axes the contact size and yield strain, for a wide range of geometries. These show the competing regimes of deformation mechanism: elastic, elastic±plastic, fully plastic similarity and ®nite deformation regime. The boundaries of the regimes depend upon the degree of strain hardening, relative size of the bodies in contact and upon their relative yield strengths. The regime of practical importance is the ®nite deformation regime for practical applications such as powder compaction. The contact force±displacement law, to be used as a part of the micromechanical constitutive model for powder compaction, is constructed semi-empirically by scaling the similarity contact law by a factor which depends on the relative size, relative yield strength and the strain hardening exponent of the bodies in contact. The accuracy of the assumption of independent contacts is addressed for the isostatic compaction of an assembly of rigid and deformable spheres, arranged in a B2 unit cell, based on two overlapping simple cubic lattices. Provided that the relative density of the compact is lower than about 0.82, the contacts deform independently