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This article describes a direct numerical homogenization method for investigating the deformation mechanisms in, and the material behaviour of metal powder during and after compaction. An assembly of elasto-plastic spherical particles in frictional contact with one another is considered, and the stress response to some prescribed deformation history as well as the resulting yield surface of the aggregate is computed with the finite-element method. This is done by applying periodic boundary conditions to the assembly, in a manner that allows arbitrary stress or strain control, and by monitoring the dissipated energies during re-loading simulations with prescribed stress space directions. Closed die and isostatic compaction are considered in particular; the resulting yield surfaces are compared and the role of plastic deformation and frictional sliding on the micro-scale is investigated. Significant deviations from isotropic phenomenological models are found and the development of anisotropy is demonstrated

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The purpose of this work is to analyze size effects in the deformation occurring during nanoindentation‐tests of thin metallic films on ceramic substrates. It is well known that classical phenomenological theories of plasticity are hardly applicable in cases of very small dimensions of a body [1]. Thus, the dependency of the mechanical behavior of thin films on the thickness can not be studied in the framework of classical theories. In order to simulate numerically the deformation, a specific material model has been chosen which is able to account for size effects. It bases on the theory of ”Mechanism Strain Gradient” (MSG) plasticity [2] in conjunction with the deformation theory of plasticity. The material model has been implemented via the user defined element subroutine (UEL) in the commercial FE code ABAQUS/Standard as a ten‐node tetrahedron‐element. With the developed subroutine the deformation of thin copper films on Si substrates during nanoindentation‐tests has been simulated. Different material models of the indentor (rigid and elastic) as well as different friction conditions between the film and the pyramidal indentor were tested. Furthermore, the influence of an additional oxide layer on the films surface has been analysed. In order to verify the numerical investigations, results from nanoindentation experiments have been used for comparison [4]. The FE simulations for different thicknesses in the range of 100‐600nm showed a very good agreement with the experiments. In particular, the size dependency of the force‐displacement curves, calculated by using the developed subroutine, is in rather good agreement with experiments. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)