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The paper deals with several aspects related to numerical modelling of material failure in strong discontinuity settings: (a) the onset and development of local material failure in terms of continuum constitutive models equipped with strain softening. Closed forms formulas for the solutions of the discontinuous material bifurcation problem are given for a class of those models; (b) finite elements with embedded discontinuities: nodal and elemental enrichments families are formulated in the continuum strong discontinuity approach (CSDA); (c) instability treatment: a discrete viscous perturbation method at the failure surfaces is presented as a way to substantially improve the robustness of the numerical simulations.

Experimental and numerical studies of powder\ud flow during the die filling stage in powder metallurgy cold\ud compaction processes are presented. An experimental setting\ud consisting of a horizontal pneumatically activated shoe,\ud a vertical die and high-speed video system has been designed.\ud The experiments show the existence of three flow regimes:\ud continuous, transitory and discrete, which are identified in\ud terms of the particle size, the morphology and the speed of\ud the shoe. In the continuous regime the powder flows in a progressive\ud manner but in the discrete one some perturbations\ud appear as a consequence of a shear band formation that forms\ud discrete avalanches. A numerical model, based on a ratedependent\ud constitutive model, via a flow formulation, and in\ud the framework of the particle finite element method (PFEM)\ud is also proposed. For the purpose of this study, the use of the\ud PFEM assumes that the powder can be modelled as a continuous\ud medium. The model, provided with the corresponding\ud characterisation of the parameters, is able to capture the two\ud fundamental phenomena observed during the filling process:\ud (1) the irreversibility of most of the deformation experienced\ud by the material and (2) the quick dissipation of the potential\ud gravitatory energy of the granular system through the inter-particle friction processes, modelled by the plastic dissipation\ud associated with the material model. Experimental and\ud numerical results have been compared in order to study the\ud viability of the proposed model.Peer ReviewedPreprin