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## Powder Compaction

This tool simulates the mechanical behavior of a binary mixture during compaction

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#### Abstract

This tool calculates the elastic and plastic deformation behavior of a single particle. The deformation behavior for a single elastic particle is determined from Hertz theory and the non-local theory. The Hertz theory is used to describe the contact behavior of an elastic particle with the classical restriction of independent contact. The non-local theory accounts for the interplay of deformations due to multiple contact forces acting on a single particle. The nonlocal theory therefore removes the classical Hertz theory restriction of independent contacts. The tool improves the nonlocal contact formulation using a higher order approximation solution of the Hertz pressure distribution. The higher order solution was obtained by correcting the description of the profiles of the surfaces in contact, by taking higher order terms in the Taylor series expansion of the profile function. The tool calculates the nondimensional pressure versus deformation and contact radius of the particle during the compaction process.

For elastic deformation the attention is restricted to elastic spheres in the absence of gravitational forces, adhesion or friction. The deformation behavior for a single plastic particle is determined from the Plastic theory.

The tool also calculates the microstructure evolution of monodisperse and polydisperse compressible granular systems at high levels of confinement.

The microstructure evolution for monodispersed systems is determined from three-dimensional particle mechanics static calculations of noncohesive frictionless monodispersed granular systems comprised by weightless spherical particles with diamameter d=0.440mm.

Two different elastic materials are considered and the die-compaction of mixtures of different volume fraction can be simulated. The walls of the cylindrical container and of the punches are assumed rigid.

Study the effect of

- die size with respect to particle size (D/d),

- material properties (Young's modulus and Poisson's ratio), and

- mixture volume fraction

on statistical features of

- the punch and die-wall pressures,

- the mechanical coordination number, and

- the network of contact forces.

The microstructure evolution for polydispersed systems is determined from three-dimensional particle mechanics static calculations of noncohesive frictionless monodispersed granular systems comprised by weightless spherical particles with diamameter ranging from 0.10 to 0.40 mm.

Powder bed is created for binary mixture of materials with particle size of individual material governed by either Gaussian distribution or Log-normal distribution. The limits for the relative standard deviation of the particle size distribution (PSD) are from 0.05 to 0.2. Two elastic materials are considered and the die-compaction for a binary mixture of materials can be simulated. The walls of the cylindrical container and of the punches are assumed rigid.

Study the effect of

- mean radius value with respect to standard deviation of the selected PSD,

- material properties (Young's modulus and Poisson's ratio), and

on statistical features of

- the punch and die-wall pressures,

- the mechanical coordination number, and

- the network of contact forces.

Also explore the effect of nonlocal mesoscopic deformations characteristic of confined granular systems by using a nonlocal contact formulation. The nonlocal contact formulation remains predictive at high levels of confinement by removing the classical assumption that contact between particles are formulated locally as independent pair-interactions.

This tool is powered by the PMA (Particle Mechanics Approach).

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PMA (Particle Mechanics Approach)

#### Credits

Acknowledgement: The following experts from the HUBzero Team have provided valuable technical input for this project, Steven Clark, Leif Delgass and Derrick Kearney.

#### References

Gonzalez, M., Cuitino, A.M. (2016). Microstructure evolution of compressible granular systems under large deformations. Journal of the Mechanics and Physics of Solids 2016; 93, 44-56

Gonzalez, M, Cuitino, A.M. (2012). A nonlocal contact formulation for confined granular systems. Journal of the Mechanics and Physics of Solids 2012; 60, 333-350

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