{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:53:49Z","timestamp":1787028829911,"version":"build-2736575974"},"reference-count":73,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T00:00:00Z","timestamp":1667174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Montanuniversitaet Leboen"},{"name":"RHI Magnesita"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The microstructures and local properties of ordinary refractory ceramic materials are heterogeneous and play a role in the fracture behavior of ordinary refractory ceramic materials. It is important to consider them in numerical modeling. Herein, the discrete element (DE) method was applied to determine the influences of heterogeneity of ordinary refractory ceramic materials by applying statistically distributed interface properties (uniform, Weibull), as opposed to constant interface properties, among the elements. Uniaxial cold crushing tests were performed as a case study. A reasonable loading strain rate for receiving quasi-static loading conditions and computation efficiency was evaluated. The loading wall displacement was recorded to present the stress\u2013strain curves of cold crushing tests. Furthermore, the effects of the interface property distributions on the load\/displacement curve, fracture energy, cold crushing strength, and fracture events were investigated. The results reveal that the DE method is a promising method for visualizing and quantifying the post\u2013peak fracture process and crack events in ordinary refractory ceramics. Different interface property distributions contribute to significant variances in the load\/displacement curve shape and fracture pattern. The heterogeneity of ordinary refractory ceramics can be further determined by comparing the experimental curves and fracture propagation along with an inverse identification approach.<\/jats:p>","DOI":"10.3390\/ma15217650","type":"journal-article","created":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T06:42:17Z","timestamp":1667371337000},"page":"7650","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Discrete Element Modelling of Cold Crushing Tests Considering Various Interface Property Distributions in Ordinary Refractory Ceramics"],"prefix":"10.3390","volume":"15","author":[{"given":"Weiliang","family":"Du","sequence":"first","affiliation":[{"name":"Department Mineral Resources Engineering, Montanuniversitaet Leoben, Peter-Tunner Strasse 5, 8700 Leoben, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6465-6285","authenticated-orcid":false,"given":"Shengli","family":"Jin","sequence":"additional","affiliation":[{"name":"Department Mineral Resources Engineering, Montanuniversitaet Leoben, Peter-Tunner Strasse 5, 8700 Leoben, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"463","DOI":"10.6028\/jres.017.021","article-title":"Young\u2019s Modulus of Elasticity, Strength, and Extensibility of Refractories in Tension","volume":"17","author":"Heindl","year":"1936","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"ref_2","first-page":"106","article-title":"Development of Nitride-Bonded SiC Refractories by MgO and Nanocomposite (MgO\/SiC) Additives","volume":"9","author":"Nourbakhsh","year":"2017","journal-title":"Refract. Worldforum."},{"key":"ref_3","first-page":"87","article-title":"Investigation of the Parameters Influencing the Refractoriness Under Load (RuL) Testing Results for Refractory Materials","volume":"7","author":"Stuppfler","year":"2015","journal-title":"Refract. Worldforum."},{"key":"ref_4","first-page":"95","article-title":"Investigation of the Factors Influencing the Bulk Density and Open Porosity Testing Results for Refractory Materials","volume":"7","author":"Dahlem","year":"2015","journal-title":"Refract. Worldforum."},{"key":"ref_5","first-page":"105","article-title":"Investigation of the Testing Parameters Influencing the Cold Crushing Strength Testing Results of Refractory Materials","volume":"7","author":"Czechowski","year":"2015","journal-title":"Refract. Worldforum."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"14662","DOI":"10.1016\/j.ceramint.2020.02.267","article-title":"Statistical study of compressive creep parameters of an alumina spinel refractory","volume":"46","author":"Samadi","year":"2020","journal-title":"Ceram. Int."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.jeurceramsoc.2019.09.010","article-title":"Mechanical and fracture investigation of magnesia refractories with acoustic emission-based method","volume":"40","author":"Dai","year":"2020","journal-title":"J. Eur. Ceram. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1080\/02726350215338","article-title":"Effects of material properties on granular flow in a silo using DEM simulation","volume":"20","author":"Xu","year":"2002","journal-title":"Part. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.powtec.2017.04.036","article-title":"DEM study on the surface mixing and whole mixing of granular materials in rotary drums","volume":"315","author":"Liu","year":"2017","journal-title":"Powder Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.ijplas.2017.07.008","article-title":"A cohesive damage-plasticity model for DEM and its application for numerical investigation of soft rock fracture properties","volume":"98","author":"Nguyen","year":"2017","journal-title":"Int. J. Plasticity"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.compgeo.2016.12.010","article-title":"Numerical modelling of desiccation cracking of clayey soil using a cohesive fracture method","volume":"85","author":"Vo","year":"2017","journal-title":"Comput. Geotech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1002\/nag.1124","article-title":"On the role of particle breakage in the shear failure behavior of granular soils by DEM","volume":"37","author":"Wang","year":"2013","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1016\/j.cma.2017.01.029","article-title":"A discrete element thermo-mechanical modelling of diffuse damage induced by thermal expansion mismatch of two-phase materials","volume":"318","author":"Levraut","year":"2017","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1016\/j.cemconcomp.2011.01.003","article-title":"A discrete element model of concrete under high triaxial loading","volume":"33","author":"Tran","year":"2011","journal-title":"Cem. Concr. Compos."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1680\/geot.1979.29.1.47","article-title":"A discrete numerical model for granular assemblies","volume":"29","author":"Cundall","year":"1979","journal-title":"Geotechnique"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0148-9062(88)92293-0","article-title":"Formulation of a three-dimensional distinct element model\u2014Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks","volume":"25","author":"Cundall","year":"1988","journal-title":"Int. J. Rock Mech. Min. Sci. Geomech. Abstr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"104476","DOI":"10.1016\/j.compgeo.2021.104476","article-title":"Effects of gravel content and shape on shear behaviour of soil-rock mixture: Experiment and DEM modelling","volume":"141","author":"Yao","year":"2022","journal-title":"Comput. Geotech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2711","DOI":"10.1007\/s11440-021-01374-8","article-title":"Micro-mechanical analysis of soil\u2013structure interface behavior under constant normal stiffness condition with DEM","volume":"17","author":"Wang","year":"2022","journal-title":"Acta Geotech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108357","DOI":"10.1016\/j.engfracmech.2022.108357","article-title":"Size effect at aggregate level in microCT scans and DEM simulation\u2013Splitting tensile test of concrete","volume":"264","author":"Suchorzewski","year":"2022","journal-title":"Eng. Fract. Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10035-014-0494-4","article-title":"A bond model for DEM simulation of cementitious materials and deformable structures","volume":"16","author":"Brown","year":"2014","journal-title":"Granul. Matter"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1016\/j.ces.2007.11.025","article-title":"A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior","volume":"63","author":"Wirtz","year":"2008","journal-title":"Chem. Eng. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10035-015-0597-6","article-title":"DEM analysis of the size effects on the behavior of crushable granular materials","volume":"18","author":"Zhou","year":"2016","journal-title":"Granul. Matter"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"17934","DOI":"10.1016\/j.ceramint.2022.03.066","article-title":"Discrete element modelling of ordinary refractory ceramics under cold crushing testing: Influence of minimum element size","volume":"48","author":"Du","year":"2022","journal-title":"Ceram. Int."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1016\/j.jeurceramsoc.2021.11.016","article-title":"Numerical modelling of the quasi-brittle behaviour of refractory ceramics by considering microcracks effect","volume":"42","author":"Asadi","year":"2022","journal-title":"J. Eur. Ceram. Soc."},{"key":"ref_25","unstructured":"Caulk, R. (2022, October 23). Stochastic Augmentation of the Discrete Element Method for the Investigation of Tensile Rupture in Heterogeneous Rock, Yade Technical Archive. Available online: https:\/\/zenodo.org\/record\/1744939#.Y14l7-RByUk."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s10035-015-0546-4","article-title":"Modelling of concrete behaviour in uniaxial compression and tension with DEM","volume":"17","author":"Nitka","year":"2015","journal-title":"Granul. Matter"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"103290","DOI":"10.1016\/j.compgeo.2019.103290","article-title":"DEM analysis on the role of aggregates on concrete strength","volume":"119","author":"Wang","year":"2020","journal-title":"Comput. Geotech."},{"key":"ref_28","unstructured":"Asadi, F., Andr\u00e9, D., Emam, S., Doumalin, P., and Huger, M. (2020, January 18\u201320). Numerical Modelling of the Quasi-Brittle Behavior Of Materials by Considering Microcracks Effect. Proceedings of the Applied Numerical Modeling in Geomechanics, Vienna, Austria."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4037","DOI":"10.1016\/j.jeurceramsoc.2014.05.034","article-title":"Compressive creep testing of refractories at elevated loads\u2014Device, material law and evaluation techniques","volume":"34","author":"Jin","year":"2014","journal-title":"J. Eur. Ceram. Soc."},{"key":"ref_30","unstructured":"Funk, J.E., and Dinger, D.R. (2013). Predictive Process Control of Crowded Particulate Suspensions: Applied to Ceramic Manufacturing, Springer Science & Business Media."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1016\/j.ijrmms.2004.09.011","article-title":"A bonded-particle model for rock","volume":"41","author":"Potyondy","year":"2004","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0167-8442(95)00008-3","article-title":"Stability of crack propagation associated with fracture energy determined by wedge splitting specimen","volume":"23","author":"Harmuth","year":"1995","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.engfracmech.2013.11.010","article-title":"Determination of Young\u2019s modulus, fracture energy and tensile strength of refractories by inverse estimation of a wedge splitting procedure","volume":"116","author":"Jin","year":"2014","journal-title":"Eng. Fract. Mech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1108\/02644400410519794","article-title":"Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme","volume":"21","author":"Bray","year":"2004","journal-title":"Eng. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1016\/j.ijimpeng.2004.03.005","article-title":"Review of experimental techniques for high rate deformation and shock studies","volume":"30","author":"Field","year":"2004","journal-title":"Int. J. Impact Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.cemconres.2014.01.013","article-title":"Compressive strength of cement paste as a function of loading rate: Experiments and engineering mechanics analysis","volume":"58","author":"Fischer","year":"2014","journal-title":"Cem. Concr. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/BF02472016","article-title":"Compressive behaviour of concrete at high strain rates","volume":"24","author":"Bischoff","year":"1991","journal-title":"Mater. Struct."},{"key":"ref_38","first-page":"364","article-title":"Effect of rate of application of load on the compressive strength of concrete","volume":"17","author":"Abrams","year":"1917","journal-title":"Proc. ASTM"},{"key":"ref_39","first-page":"380","article-title":"The effect of testing speed on strength and elastic properties of concrete","volume":"36","author":"Jones","year":"1936","journal-title":"Proc. ASTM"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1680\/ijoti.1942.13813","article-title":"Effect of rate of loading on the mechanical properties of some materials","volume":"18","author":"Evans","year":"1942","journal-title":"J. Inst. Civ. Eng."},{"key":"ref_41","first-page":"268","article-title":"On the elastic and plastic properties of concrete in compression tests with high deformation velocity, part 1","volume":"29","author":"Katsuta","year":"1943","journal-title":"Trans. Inst. Jap. Arch."},{"key":"ref_42","first-page":"11","article-title":"Rate of loading for compressive strength tests","volume":"38","author":"Thaulow","year":"1953","journal-title":"Betong"},{"key":"ref_43","first-page":"729","article-title":"Effect of straining rate on the compressive strength and elastic properties of concrete","volume":"49","author":"Watstein","year":"1953","journal-title":"J. Proc."},{"key":"ref_44","first-page":"19","article-title":"Dynamical compressive deformation and failure of concrete under earthquake load","volume":"67","author":"Hatano","year":"1960","journal-title":"Trans. Jpn. Soc. Civ. Eng."},{"key":"ref_45","unstructured":"Ban, S. (1960, January 11\u201318). Behaviour of plain concrete under dynamic loading with straining rate comparable to earthquake loading. Proceedings of the 2\u2019nd World Conference on Earthquake Engineering, Tokyo, Japan."},{"key":"ref_46","unstructured":"Takeda, J.I., and Tachikawa, H. (1972, January 1). Deformation and fracture of concrete subjected to dynamic load. Proceedings of the Conference on Mechanical Behavior of Materials, Kyoto, Japan."},{"key":"ref_47","unstructured":"Lundeen, R.L. (1963). Dynamic and Static Tests of Plain Concrete Specimens, Report 1, Army Engineer Waterways Experiment Station. Available online: https:\/\/apps.dtic.mil\/sti\/citations\/AD0752803."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"498","DOI":"10.2472\/jsms.14.141Appendix_498","article-title":"On mechanical behavior of rock under various loading rates","volume":"14","author":"Horibe","year":"1965","journal-title":"J. Soc. Mater. Sci."},{"key":"ref_49","unstructured":"Cowell, W.L. (1966). Dynamic Properties of Plain Portland Cement Concrete, Naval Civil Engineering Lab Port. Available online: https:\/\/apps.dtic.mil\/sti\/citations\/AD0635055."},{"key":"ref_50","first-page":"745","article-title":"Strength and energy absorption capabilities of plain concrete under dynamic and static loadings","volume":"64","author":"Atchley","year":"1967","journal-title":"J. Proc."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1680\/macr.1972.24.78.25","article-title":"Concrete subjected to high rates of loading in compression","volume":"24","author":"Hughes","year":"1972","journal-title":"Mag. Concr. Res."},{"key":"ref_52","unstructured":"Millstein, L., and Sabnis, G.M. (1982, January 2\u20134). Concrete strength under impact loading. Proceedings of the Concrete Structures under Impact and Impulsive Loading, Berlin, Germany. Available online: https:\/\/inis.iaea.org\/search\/search.aspx?orig_q=RN:14720296."},{"key":"ref_53","unstructured":"Bertero, V.V., Rea, D., Mahin, S., and Atalay, M.B. (1973, January 25\u201329). Rate of loading effects on uncracked and repaired reinforced concrete members. Proceedings of the Fifth World Conference on Earthquake Engineering, Rome, Italy."},{"key":"ref_54","first-page":"212","article-title":"The effect of loading rate on compressive strength and modulus of elasticity of concrete","volume":"14","author":"Wesche","year":"1972","journal-title":"Materialpruefung"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1680\/macr.1973.25.83.73","article-title":"The effect of rate of loading upon the static and fatigue strengths of plain concrete in compression","volume":"25","author":"Sparks","year":"1973","journal-title":"Mag. Concr. Res."},{"key":"ref_56","unstructured":"Bresler, B., and Bertero, V.V. (1975, January 5\u20136). Influence of high strain rate and cyclic loading of unconfined and confined concrete in compression. Proceedings of the 2nd Canadian Conference on Earthquake Engineering, Hamilton, ON, USA."},{"key":"ref_57","unstructured":"Hjorth, O. (1976). [A Contribution to the Problem of Strength and Bond Relationships for Steel and Concrete at High Loading Rates, Doctoral dissertation, Braunschweig Universitaet of Technology]."},{"key":"ref_58","unstructured":"Kvirikadze, O.P. (1977, January 5\u20139). Determination of the ultimate strength and modulus of deformation of concrete at different rates of loading. Proceedings of the International Symposium, Testing In-Situ of Concrete Structures, Budapest, Hungry."},{"key":"ref_59","unstructured":"Popp, C. (1977). Untersuchungen \u00dcber Das Verhalten Von Beton Bei Schlagartiger Beanspruchung, Ernst in Komm."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1680\/macr.1978.30.105.189","article-title":"Compressive strength and ultimate strain of concrete under impact loading","volume":"30","author":"Hughes","year":"1978","journal-title":"Mag. Concr. Res."},{"key":"ref_61","first-page":"434","article-title":"Betongs slagh\u00e5llfasthet: Impact strength of concrete","volume":"79","author":"Fagerlund","year":"1979","journal-title":"Cem. -Och Betonginst"},{"key":"ref_62","first-page":"225","article-title":"Concrete under very short-term loading","volume":"32","author":"Paulmann","year":"1982","journal-title":"Betong"},{"key":"ref_63","first-page":"393","article-title":"Mechanical behaviour of some construction materials subjected to rapid loading and low temperature","volume":"50","author":"Rostasy","year":"1984","journal-title":"Betonw. + Fert. -Tech."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0262-5075(85)90023-5","article-title":"Compressive strength and deformation of steel fibre reinforced concrete under high rate of strain","volume":"7","author":"Rostasy","year":"1985","journal-title":"Int. J. Cem. Compos. Lightweight Concr."},{"key":"ref_65","first-page":"73","article-title":"Ductility of plain and confined concrete under different strain rates","volume":"81","author":"Dilger","year":"1984","journal-title":"J. Proc."},{"key":"ref_66","unstructured":"Malvern, L.E., and Ross, C.A. (1986). Dynamic Response of Concrete and Concrete Structures, Florida University Gainesville, Department of Engineering Sciences. Available online: https:\/\/apps.dtic.mil\/sti\/citations\/ADA173082."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1260\/2041-4196.1.1.145","article-title":"Numerical analysis of lateral inertial confinement effects on impact test of concrete compressive material properties","volume":"1","author":"Hao","year":"2010","journal-title":"Int. J. Prot. Struct."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"021309","DOI":"10.1103\/PhysRevE.72.021309","article-title":"Rheophysics of dense granular materials: Discrete simulation of plane shear flows","volume":"72","author":"Cruz","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.powtec.2018.12.024","article-title":"Influence of quasi-static loading rates on crushable granular materials: A DEM analysis","volume":"344","author":"Das","year":"2019","journal-title":"Powder Technol."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1140\/epje\/i2003-10153-0","article-title":"On dense granular flows","volume":"14","author":"Midi","year":"2004","journal-title":"Eur. Phys. J. E"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"058101","DOI":"10.1063\/1.2722242","article-title":"Dense flows of bidisperse assemblies of disks down an inclined plane","volume":"19","author":"Rognon","year":"2007","journal-title":"Phys. Fluids"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1007\/s40571-020-00361-2","article-title":"DEM simulations of polydisperse media: Efficient contact detection applied to investigate the quasi-static limit","volume":"8","author":"Shire","year":"2021","journal-title":"Comput. Part. Mech."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Modenese, C., Utili, S., and Houlsby, G.T. (2012). A Numerical Investigation of Quasi-Static Conditions for Granular Media. Discrete Element Modelling Particulate Media, Royal Society of Chemistry.","DOI":"10.1039\/9781849735032-00187"}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/21\/7650\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:06:35Z","timestamp":1760144795000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/21\/7650"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,31]]},"references-count":73,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["ma15217650"],"URL":"https:\/\/doi.org\/10.3390\/ma15217650","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,31]]}}}