{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T20:37:12Z","timestamp":1790023032204,"version":"4.0.1"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:00:00Z","timestamp":1578700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The confined uniaxial tests of packings with discrete particle size distribution (PSD) were modeled with the discrete element method. Ternary packings of spheres with PSD uniform or nonuniform by number of particles were examined in three-dimensional (3D) system. The study addressed an effect of the particle size ratio and the particle size fraction on structural and micromechanical properties of mixtures. A study of packing structure included porosity and coordination numbers, while the investigation of micromechanical properties included distribution of normal contact forces and stress transmission through the packing. A micro-scale investigation of the effect of particle size ratio on structure and mechanics of the ternary packings revealed a strong relationship between the properties of sample and the value of parameter till its critical value was reached. A further increase in particle size ratio did not significantly affect properties of packings. Contrary to the porosity and coordination numbers, the partial stresses were highly affected by the fraction of particle size classes in ternary mixtures. The contribution of the partial stress into the global stress was determined by number fraction of particles in packings with small particle size ratio, while it was mainly determined by particle size ratio in packings with small particle size ratio.<\/jats:p>","DOI":"10.3390\/ma13020339","type":"journal-article","created":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T04:05:51Z","timestamp":1578888351000},"page":"339","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Structural and Micromechanical Properties of Ternary Granular Packings: Effect of Particle Size Ratio and Number Fraction of Particle Size Classes"],"prefix":"10.3390","volume":"13","author":[{"given":"Joanna","family":"Wi\u0105cek","sequence":"first","affiliation":[{"name":"Institute of Agrophysics, Polish Academy of Sciences, Do\u015bwiadczalna 4, 20-290 Lublin 27, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mateusz","family":"Stasiak","sequence":"additional","affiliation":[{"name":"Institute of Agrophysics, Polish Academy of Sciences, Do\u015bwiadczalna 4, 20-290 Lublin 27, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jalal","family":"Kafashan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering in Agro-Machinery &amp; Mechanization, Agricultural Engineering Research Institute (AERI), Agricultural Research Education and Extension Organization (AREEO), 31359-33151 Karaj, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1111\/j.1151-2916.1961.tb13716.x","article-title":"Mechanical Packing of Spherical Particles","volume":"44","author":"McGeary","year":"1961","journal-title":"J. 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