The finite-element method is used to perform an accurate numerical study of the normal indentation of an elastic-plastic half-space by a rigid sphere. The effects of elasticity and strain-hardening rate of the half-space are explored, and the role of friction is assessed by analysing the limiting cases of frictionless contact and sticking friction. Indentation maps are constructed with axes of contact radius a (normalized by the indenter radius R) and the yield strain of the half-space. Competing regimes of deformation mode are determined and are plotted on the indentation map: (i) elastic Hertzian contact; (ii) elastic-plastic deformation; (iii) plastic similarity regime; (iv) finite-deformation elastic contact; and (v) finite-deformation plastic contact. The locations of the boundaries between deformation regimes change only slightly with the degree of strain-hardening rate and of interfacial friction. It is found that the domain of validity of the rigid-strain-hardening similarity solution is rather restricted: it is relevant only for solids with a yield strain of less than 2 × 10 −4 and a/R < 0.16. Friction between the indenter and the substrate strongly affects the strain field beneath the indenter, and has a significant effect on the contact size as a function of indent depth. The effect of pre-stress within the half-space is also explored; it is found that the indentation response is hardly affected, except for the case of the elastic-plastic indentation regime.

A ®nite element study is performed on the frictionless normal contact of elastic±plastic spheres and rigid spheres. The eects 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. Ó

Complex structures consisting of intertwined, nominally vertical carbon nanotubes (CNTs), referred to as turfs, have unique properties that arise from their complex nanogeometry and interactions between individual CNT segments. For applications such as contact switches for electrical or thermal transfer it is necessary to understand the properties that arise from the collective behavior of an assemblage of CNTs rather than the properties of a single tube. In this study, the mechanical response of turfs bonded to substrates under compressive loading is demonstrated experimentally; coordinated alignment and buckling takes place under uniform loads. The mechanical response of turf structures provides some surprising results regarding parameters that control permanent deformation and buckling in assemblages of nanostructures; buckling of the turf structure is controlled by the height and effective modulus of the turf, but not the aspect ratio of the structure. We present and verify a model which describes the coordinated buckling phenomena relevant for applications such as CNT turfs for thermal transfer media.

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