This tool is powered by the PMA (Particle Mechanics Approach), which includes three simulation types: (i) - Single-particles, (ii) - Monodispersed Powder Bed, and (iii) - Polydispersed Powder bed. The tool also include three distinct material behaviors: (i) - elastic, (ii) - plastic and (iii) - elastoplastic. Please refer to the following publications for further details about these contact formulations and numerical methods:

[1] Gonzalez M. and Cuitiño, A.M., “A nonlocal contact formulation for confined granular systems”, Journal of the Mechanics and Physics of Solids, 60, 333-350, 2012. 

[2] Gonzalez M. and Cuitiño A.M., “Microstructure evolution of compressible granular systems under large deformations”, Journal of the Mechanics and Physics of Solids, 93, 44-56, 2016. 

[3] Gonzalez M., Poorsolhjouy P., Thomas A., Liu J., and Balakrishnan, “Statistical characterization of microstructure evolution during compaction of granular systems composed of spheres with hardening plastic behavior”, Mechanics Research Communications, 92, 131-136, 2018.

[4] Agarwal A. and Gonzalez M., “Contact radius and curvature corrections to the nonlocal contact formulation accounting for multi-particle interactions in elastic confined granular systems”, International Journal of Engineering Science, 133, 26-46, 2018. 

[5] Gonzalez M., “Generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength”, Journal of the Mechanics and Physics of Solids, 122, 633-656, 2019. 

Single-particle: This tool calculates the elastic and plastic deformation behavior of a single particle (Elastoplastic behavior is not included for this simulation type). The deformation behavior for a single elastic particle is determined from the 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 non-local theory, therefore, removes the classical Hertz theory restriction of independent contacts. The tool improves the non-local 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. Four loading configurationsare available, namely, simple compression, two-wall die compression, four-wall die compression, and hydrostatic compression. See [1] and [4].

The behavior of multiple particles interacting with each other under a compressive force if often of interest in many industries and research fields. The next two types of simulations available - Monodispersed Powder Bed, and Polydispersed Powder bed - address this problem for a simple cylindrical rigid die, and thus a cylindrical compact or tablet. The fabrication of a tablet resumes to the operation involves combining a mixture of powdered substances into a single bonded compact, or tablet, through the application of compressive forces. The process mainly consists of four stages: die filling, compaction, unloading, and ejection. During the compaction, particles are rearranged and undergo elastic and plastic deformation, which leads to particle-particle bonds formation. In the last two steps, the whole compact experiences elastic relaxation after being plastically deformed during fabrication. It is well known that the performance of compacted particulate products is directly related to their microstructure. The tool includes a particle mechanics approach (PMA) to model the compaction process using generalized loading-unloading contact laws for elastoplastic spheres with bonding strength. The microstructure evolution of monodisperse and polydisperse compressible granular systems at high levels of confinement and upon to unloading of the compressive punch are tracked in the simulations, that is, ejection is not included in the simulation (yet).

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

Two different materials are considered, and the die-compaction of mixtures* of different volume fractions can be simulated. The walls of the cylindrical container and 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, etc.), and

 - mixture volume fraction 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 non-local mesoscopic deformations characteristic of confined granular systems by using a non-local contact formulation. The non-local contact formulation remains predictive at high levels of confinement by removing the classical assumption that contact between particles is formulated locally as independent pair-interactions. See [1], [2] and [4].

Polydispersed Powder bed: The microstructure evolution for polydispersed systems is determined from three-dimensional particle mechanics static calculations of noncohesive frictionless granular systems comprised of weightless spherical particles with diameters ranging from 0.00 to 0.60 mm**.

The powder bed is created for a binary mixture* of materials with a 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 0.9. Two materials are considered, and the die-compaction for a binary mixture of materials can be simulated (the non-local formulation for elastic deformation is not include for this simulation type). The walls of the cylindrical container and the punches are assumed rigid.  See [3] and [5].

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, etc.), and

on statistical features of

 - the punch and die-wall pressures,

 - the mechanical coordination number, and

 - the network of contact forces.

We anticipate that our tool will provide the research community and classrooms the means to better understand the underlying mechanics of compaction, up to porosities close to zero, and we demonstrate that seamless integration of experimental and computational methods is paramount for the development of the powder compaction field.

*for single material just enter the same material properties and an arbitrary volume fraction

**the tool limits the maximum amount of particle inside the die to 5000.”

PMA (Particle Mechanics Approach)

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

[1] Gonzalez M. and Cuitiño, A.M., “A nonlocal contact formulation for confined granular systems”, Journal of the Mechanics and Physics of Solids, 60, 333-350, 2012. 

[2] Gonzalez M. and Cuitiño A.M., “Microstructure evolution of compressible granular systems under large deformations”, Journal of the Mechanics and Physics of Solids, 93, 44-56, 2016. 

[3] Gonzalez M., Poorsolhjouy P., Thomas A., Liu J., and Balakrishnan, “Statistical characterization of microstructure evolution during compaction of granular systems composed of spheres with hardening plastic behavior”, Mechanics Research Communications, 92, 131-136, 2018.

[4] Agarwal A. and Gonzalez M., “Contact radius and curvature corrections to the nonlocal contact formulation accounting for multi-particle interactions in elastic confined granular systems”, International Journal of Engineering Science, 133, 26-46, 2018. 

[5] Gonzalez M., “Generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength”, Journal of the Mechanics and Physics of Solids, 122, 633-656, 2019. 

Researchers should cite this work as follows:

• [1] Gonzalez M. and Cuitiño, A.M., “A nonlocal contact formulation for confined granular systems”, Journal of the Mechanics and Physics of Solids, 60, 333-350, 2012. 

  [2] Gonzalez M. and Cuitiño A.M., “Microstructure evolution of compressible granular systems under large deformations”, Journal of the Mechanics and Physics of Solids, 93, 44-56, 2016. 

  [3] Gonzalez M., Poorsolhjouy P., Thomas A., Liu J., and Balakrishnan, “Statistical characterization of microstructure evolution during compaction of granular systems composed of spheres with hardening plastic behavior”, Mechanics Research Communications, 92, 131-136, 2018.

  [4] Agarwal A. and Gonzalez M., “Contact radius and curvature corrections to the nonlocal contact formulation accounting for multi-particle interactions in elastic confined granular systems”, International Journal of Engineering Science, 133, 26-46, 2018. 

  [5] Gonzalez M., “Generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength”, Journal of the Mechanics and Physics of Solids, 122, 633-656, 2019. 

• Chen Shang, Yuqi Fang, Carlos E Fernandez-Caban, Wentao Chen, Ayush Giri, Caroline Baker, Yasasvi Raghavendra Bommireddy, Ankit Agarwal, Marcial Gonzalez, Jesse Lee Hoffman, Isabel Bojanini, Melanie Hacopian, Vidal Lopez, Pedro Henrique Cidreiro Martins, Paul Beckwith (2019), "Powder Compaction," https://nanohub.org/resources/gscompaction. (DOI: 10.21981/SYT1-MN34).

  BibTex | EndNote

1. binary polydisperse mixture
2. compaction
3. granular system
4. Hertz Theory
5. materials science
6. NCN Group - Materials Science
7. nonlocal contact formulation
8. powder compaction