# Open-source support toward validating and falsifying discrete mechanics models using synthetic granular materials—Part I: Experimental tests with particles manufactured by a 3D printer

- 250 Downloads

## Abstract

This article presents a new test prototype that leverages the 3D printing technique to create artificial particle assembles to provide auxiliary evidences that supports the validation procedure. The prototype test first extracts particle shape features from micro-CT images of a real sand grain and replicates the geometrical features of sand grain using a 3D printer. The quantitative measurements of the particle shape descriptors reveal that the synthetic particles inherit some attributes such as aspect ratio and sparseness of the real materials while exhibiting marked differences for sphericity and convexity. While it is not sufficient to consider the printed particle assembles a replica of the real sand, the repeatable manufacture process provides convention tools to generate additional data that supports the validation procedure for particulate simulations. Oedometric compression tests are conducted on a specimen composed of the printed particles of identical size and shape to create benchmark cases for calibrating and validating discrete element models. Results from digital image correlation on the synthetic sand assemblies reveal that the fracture and fragmentation of the synthetic particles are minor, which in return makes particle position tracking possible. As our prototype test and research data are designed to be open source, the dataset and the prototype work will open doors for modelers to design further controlled experiments using synthetic granular materials such that the individual influence of each morphological feature of granular assemblies (e.g., shape and size distribution, void ratio, fabric orientation) can be individually tested without being simultaneously affected by other variables.

## Keywords

3D printing Compression and recompression index Discrete DIC Oedometer test Open-source data for inverse problems X-ray CT## Notes

### Acknowledgements

We thank the two anonymity reviewers for the constructive suggestions and feedback that leads to improvements of this article. This research is supported by the Earth Materials and Processes program from the US Army Research Office under Grant Contract W911NF-15-1-0442 and W911NF-15-1-0581, the Dynamic Materials and Interactions Program from the Air Force Office of Scientific Research under Grant Contract FA9550-17-1-0169, the nuclear energy university program from department of energy under Grant Contract DE-NE0008534. These supports are gratefully acknowledged. The views and conclusions contained in this document are those of the authors, and should not be interpreted as representing the official policies, either expressed or implied, of the sponsors, including the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

## References

- 1.Andò E, Hall S, Viggiani G, Desrues J, Bésuelle P (2012) Experimental micromechanics: grain-scale observation of sand deformation. Géotech Lett 2(3):107–112CrossRefGoogle Scholar
- 2.Andò E, Hall SA, Viggiani G, Desrues J, Bésuelle P (2012) Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach. Acta Geotech 7(1):1–13CrossRefGoogle Scholar
- 3.Andrade JE, Avila CF, Hall SA, Lenoir N, Viggiani G (2011) Multiscale modeling and characterization of granular matter: from grain kinematics to continuum mechanics. J Mech Phys Solids 59(2):237–250CrossRefzbMATHGoogle Scholar
- 4.Andrade JE, Lim K-W, Avila CF, Vlahinić I (2012) Granular element method for computational particle mechanics. Comput Methods Appl Mech Eng 241:262–274CrossRefzbMATHGoogle Scholar
- 5.Athanassiadis AG, Miskin MZ, Kaplan P, Rodenberg N, Lee SH, Merritt J, Brown E, Amend J, Lipson H, Jaeger HM (2014) Particle shape effects on the stress response of granular packings. Soft Matter 10(1):48–59CrossRefGoogle Scholar
- 6.Azeiteiro RJ, Coelho PA, Taborda DM, Grazina JC (2017) Critical state-based interpretation of the monotonic behavior of Hostun sand. J Geotech Geoenviron Eng 143(5):04017004CrossRefGoogle Scholar
- 7.Cho GC, Dodds J, Santamarina JC (2004) Particle shape effects on packing density. Stiffness and Strength of Natural and Crushed Sands-Internal Report, Georgia Institute of TechnologyGoogle Scholar
- 8.Colliat-Dangus J-L (1986) Comportement des matériaux granulaires sous fortes contraintes: influence de la nature minéralogique du matériau étudié. Ph.D. thesis, Grenoble 1Google Scholar
- 9.Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
- 10.Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Methods Geomech 28(4):279–321CrossRefGoogle Scholar
- 11.Fang Q, Boas DA (2009) Tetrahedral mesh generation from volumetric binary and grayscale images. In: IEEE international symposium on biomedical imaging: from nano to macro, 2009. ISBI’09. IEEE, pp 1142–1145Google Scholar
- 12.Favier JF, Abbaspour-Fard MH, Kremmer M, Raji AO (1999) Shape representation of axi-symmetrical, non-spherical particles in discrete element simulation using multi-element model particles. Eng Comput 16(4):467–480CrossRefzbMATHGoogle Scholar
- 13.Flavigny E, Desrues J, Palayer B (1990) Note technique: le sable d’hostun RF. Revue française de géotechnique 53:67–70CrossRefGoogle Scholar
- 14.Friedman JH (1997) On bias, variance, 0/1—loss, and the curse-of-dimensionality. Data Min Knowl Discov 1(1):55–77CrossRefGoogle Scholar
- 15.Hall SA, Bornert M, Desrues J, Pannier Y, Lenoir N, Viggiani G, Bésuelle P (2010) Discrete and continuum analysis of localised deformation in sand using X-ray \(\mu\)CT and volumetric digital image correlation. Géotechnique 60(5):315–322CrossRefGoogle Scholar
- 16.Hanaor AH, Gan Y, Revay M, Airey DW, Einav I (2016) 3D printable geomaterials. Géotechnique 66:323–332CrossRefGoogle Scholar
- 17.Henann DL, Kamrin K (2013) A predictive, size-dependent continuum model for dense granular flows. Proc Natl Acad Sci 110(17):6730–6735MathSciNetCrossRefzbMATHGoogle Scholar
- 18.Johnson KL (1987) Contact mechanics. Cambridge University Press, CambridgeGoogle Scholar
- 19.Katagiri J, Matsushima T, Yamada Y (2010) Simple shear simulation of 3D irregularly-shaped particles by image-based DEM. Granul Matter 12(5):491–497CrossRefzbMATHGoogle Scholar
- 20.Keller T, Lamandé M, Schjønning P, Dexter AR (2011) Analysis of soil compression curves from uniaxial confined compression tests. Geoderma 163(1):13–23CrossRefGoogle Scholar
- 21.Kuhn MR, Sun W, Wang Q (2015) Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability. Acta Geotech 10(4):399–419CrossRefGoogle Scholar
- 22.Lancelot L, Shahrour I, Al Mahmoud M (2003) Experimental study of sand behaviour at low stresses. In: Di Benedetto et al (eds) Deformation characteristics of geomaterials. Swets & Zeitlinger B.V., Lisse, The Netherlands, pp 655–662Google Scholar
- 23.Liu Y, Sun W, Yuan Z, Fish J (2015) A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials. Int J Numer Methods Eng 106:129–160MathSciNetCrossRefzbMATHGoogle Scholar
- 24.Liu Y, Sun W, Fish J (2016) Determining material parameters for critical state plasticity models based on multilevel extended digital database. J Appl Mech 83(1):011003CrossRefGoogle Scholar
- 25.Matuttis HG, Nobuyasu Ito, Alexander Schinner (2003) Effect of particle shape on bulk-stress–strain relations of granular materials. In: Proceedings of RIMS symposium on mathematical aspects of complex fluids III, RIMS Kokyoroku series, vol 1305, pp 89–99Google Scholar
- 26.Miskin MZ, Jaeger HM (2013) Adapting granular materials through artificial evolution. Nat Mater 12(4):326–331CrossRefGoogle Scholar
- 27.Ng T-T (2006) Input parameters of discrete element methods. J Eng Mech 132(7):723–729CrossRefGoogle Scholar
- 28.Nouguier-Lehon C, Cambou B, Vincens E (2003) Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis. Int J Numer Anal Methods Geomech 27(14):1207–1226CrossRefzbMATHGoogle Scholar
- 29.Oda M, Konishi J, Nemat-Nasser S (1982) Experimental micromechanical evaluation of strength of granular materials: effects of particle rolling. Mech Mater 1(4):269–283CrossRefGoogle Scholar
- 30.Oda M, Nemat-Nasser S, Konishi J (1985) Stress-induced anisotropy in granular masses. Soils Found 25(3):85–97CrossRefGoogle Scholar
- 31.Ouhbi N, Voivret C, Perrin G, Roux JN (2017) 3D particle shape modelling and optimization through proper orthogonal decomposition. Granul Matter 19(4):86CrossRefGoogle Scholar
- 32.Pena AA, Garcia-Rojo R, Herrmann HJ (2007) Influence of particle shape on sheared dense granular media. Granul Matter 9(3–4):279–291CrossRefzbMATHGoogle Scholar
- 33.Pestana JM, Whittle AJ, Salvati LA (2002) Evaluation of a constitutive model for clays and sands: Part I—sand behaviour. Int J Numer Anal Methods Geomech 26(11):1097–1121CrossRefzbMATHGoogle Scholar
- 34.Sadrekarimi A, Olson SM (2011) Critical state friction angle of sands. Géotechnique 61(9):771–783CrossRefGoogle Scholar
- 35.Santamarina JC, Cho GC (2001) Determination of critical state parameters in sandy soils—simple procedure. Geotech Test J 24:185–192CrossRefGoogle Scholar
- 36.Schneider CA, Rasband WS, Eliceiri KW (2012) NIH image to ImageJ: 25 years of image analysis. Nat Methods 9(7):671CrossRefGoogle Scholar
- 37.Schofield A, Wroth P (1968) Critical state soil mechanics, vol 310. McGraw-Hill, LondonGoogle Scholar
- 38.Shin H, Santamarina JC (2012) Role of particle angularity on the mechanical behavior of granular mixtures. J Geotech Geoenviron Eng 139(2):353–355CrossRefGoogle Scholar
- 39.Sun W, Andrade JE, Rudnicki JW (2011) Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability. Int J Numer Methods Eng 88(12):1260–1279MathSciNetCrossRefzbMATHGoogle Scholar
- 40.Sun W (2013) A unified method to predict diffuse and localized instabilities in sands. Geomech Geoeng 8(2):65–75CrossRefGoogle Scholar
- 41.Sun W, Wong TF (2018) Prediction of permeability and formation factor of sandstone with hybrid lattice Boltzmann/finite element simulation on microtomographic images. Int J Rock Mech Min Sci 106:269–277Google Scholar
- 42.Sun W, Andrade JE, Rudnicki JW, Eichhubl P (2011) Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations. Geophys Res Lett 38(10):L10302CrossRefGoogle Scholar
- 43.Sun W, Kuhn MR, Rudnicki JW (2013) A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band. Acta Geotech 8(5):465–480CrossRefGoogle Scholar
- 44.Tudisco E, Hall SA, Charalampidou EM, Kardjilov N, Hilger A, Sone H (2015) Full-field measurements of strain localisation in sandstone by neutron tomography and 3D-volumetric digital image correlation. Phys Procedia 69:509–515CrossRefGoogle Scholar
- 45.Tudisco E, Andò E, Cailletaud R, Hall SA (2017) Tomowarp2: a local digital volume correlation code. SoftwareX 6:267–270CrossRefGoogle Scholar
- 46.Wadell H (1935) Volume, shape, and roundness of quartz particles. J Geol 43(3):250–280CrossRefGoogle Scholar
- 47.Wang B, Chen Y, Wong T (2008) A discrete element model for the development of compaction localization in granular rock. J Geophys Res Solid Earth 113(B3):B03202CrossRefGoogle Scholar
- 48.Wang K, Sun W (2015) Anisotropy of a tensorial Bishop’s coefficient for wetted granular materials. J Eng Mech 143:B4015004CrossRefGoogle Scholar
- 49.Wang K, Sun W (2016) A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain. Comput Methods Appl Mech Eng 304:546–583MathSciNetCrossRefGoogle Scholar
- 50.Wang K, Sun W (2016) A semi-implicit micropolar discrete-to-continuum method for granular materials. In: Papadrakakis M, Papadopoulos V, Stefanou G, Plevris V (eds) Proceedings of European Congress on computational methods in applied science and engineering, June, pp 5–10, Crete IslandGoogle Scholar
- 51.Wang K, Sun W (2018) A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning. Comput Methods Appl Mech Eng 334:337–380MathSciNetCrossRefGoogle Scholar
- 52.Wang K, Sun W, Salager S, Na S, Khaddour G (2016) Identifying material parameters for a micro-polar plasticity model via X-ray micro-computed tomographic (CT) images: lessons learned from the curve-fitting exercises. Int J Multiscale Comput Eng 14(4):389–413CrossRefGoogle Scholar
- 53.Wood DM (1990) Soil behaviour and critical state soil mechanics. Cambridge University Press, CambridgezbMATHGoogle Scholar
- 54.Xu YF, Sun DA (2005) Correlation of surface fractal dimension with frictional angle at critical state of sands. Geotechnique 55(9):691–695CrossRefGoogle Scholar