Computational Physics Group

Karel Matous










A poro-viscoplastic constitutive model for cold compacted powders at finite strains

A. Krairi1, K. Matous1,2 and A. Salvadori1,2

1Center for Shock Wave-processing of Advanced Reactive Materials,
2Department of Aerospace and Mechanical Engineering,
University of Notre Dame, Notre Dame, IN, 46556, USA.


    A novel finite strain poro-viscoplastic phenomenological model for cold compacted materials is proposed. The model relies on the three-stage density evolution paradigm and describes the material evolution from loose to solid state. This model accounts for rate dependence, elasto-plastic coupling, pressure sensitivity, and transition to full solid state. The model has been implemented, verified, and validated against experimental data available in the literature for copper powder compounds.


    A novel phenomenological constitutive model for cold compacted materials has been developed. The transition of the material state from loose powder to full solid is described by three stages: granule sliding and rearrangement, granule deformation, and granule densification and hardening. The cohesion between the grains as well as the elastic properties are monotonically increasing as a function of an internal variable related to the forming pressure, which evolves with the irreversible volumetric change of the material. The model is expressed within the framework of large deformations, stemming from the multiplicative decomposition of the total deformation gradient into elastic and plastic parts. It couples pressure dependence and viscoplasticity under arbitrary loadings.
    The proposed Helmholtz free energy resembles the classical neo-hookean one. However, the elastic properties evolve with an internal variable, which corresponds to the exerted forming pressure (phenomena known as the elasto-plastic coupling). The plastic evolution is governed by rate-dependent, power-law flow rules for the volumetric and isochoric parts of the strain. The evolution of the forming pressure is related to the plastic deformation, which has a micro-mechanical nature.
    An explicit numerical algorithm has been developed and implemented. Detailed model calibration has been described. Next, numerical predictions have been validated against experimental tests available in the literature on copper powders. Good agreement between model predictions and experimental results has been found, thus emphasizing the potential of the proposed model.
    Simulations under complex loading histories, coupling triaxial pressure and shear, have shown the response of the model when the material density after compaction equals to that of a solid. In such a case, the final shear viscoplastic limit is reached and the cold-compacted powder behaves like a full solid material with a perfectly plastic response. A similar behavior in shear has been observed when compacting below the full solid state, namely a perfectly plastic like response at a shear stress level equal to the shear strength gained during the compaction process.
    Complex micromechanical features such as grain crushing or particles densification have not been explicitly included in the model. Investigating those phenomena could enrich our phenomenological model, which is tailored for large industrial applications.


    This work was supported by the Department of Energy, National Nuclear Security Administration, under the award number DE-NA0002377 as part of the Predictive Science Academic Alliance Program II.

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(c) 2017 Notre  Dame  and Dr. Karel Matous