zbMATH — the first resource for mathematics

A generic computational model for three-dimensional fracture and fragmentation problems of quasi-brittle materials. (English) Zbl 07305805
Summary: Fracture and fragmentation in three dimensions are of great importance to understand the mechanical behaviour of quasi-brittle materials in failure stress states. In this paper, a generic computational model has been developed in an in-house C/C++ code using the combined finite-discrete element method, which is capable of modelling the entire three-dimensional fracturing process, including pre-peak hardening deformation, post-peak strain softening, transition from continuum to discontinuum, and explicit interaction between discrete fragments. The computational model is validated by Brazilian tests and polyaxial compression tests, and a realistic multi-layer rock model in an in situ stress condition is presented as an application example. The results show that the computational model can capture both continuum and discontinuum behaviour and therefore it provides an ideal numerical tool for fracture and fragmentation problems.
Reviewer: Reviewer (Berlin)
74 Mechanics of deformable solids
DEMPack; Y-Geo
Full Text: DOI
[1] Andrade, J. E.; Avila, C. F.; Hall, S. A.; Lenoir, N.; Viggiani, G., Multiscale modelling and characterization of granular matter: from grain kinematics to continuum mechanics, J. Mech. Phys. Solid., 59, 237-250 (2011) · Zbl 1270.74049
[2] Arthur, J. R.F.; Dunstan, T.; Al-Ani, Q. A.J. L.; Assadi, A., Plastic deformation and failure in granular media, Geotechnique, 27, 1, 53-74 (1977)
[3] Atkinson, B. K., Fracture Mechanics of Rock (1987), Academic Press
[4] Kh; Bagherzadeh, A.; Mirghasemi, A. A.; Mohammadi, S., Micromechanics of breakage in sharp-edge particles using combined DEM and FEM, Particuology, 6, 347-361 (2008)
[5] Kh; Bagherzadeh, A.; Mirghasemi, A. A.; Mohammadi, S., Numerical simulation of particle breakage of angular particles using combined DEM and FEM, Powder Technol., 205, 15-29 (2011)
[6] Baraldi, D.; Cecchi, A.; Tralli, A., Continuous and discrete models for masonry like material: a critical comparative study, Eur. J. Mech. Solid., 50, 39-58 (2015) · Zbl 1406.74037
[7] Beex, L. A.A.; Peerlings, R. H.J.; Geers, M. G.D., A multiscale quasicontinuum method for dissipative lattice models and discrete networks, J. Mech. Phys. Solid., 64, 154-169 (2014)
[8] Belayneh, M.; Cosgrove, J. W., Fracture-pattern variations around a major fold and their implications regarding fracture prediction using limited data: an example from the Bristol Channel Basin, Geological Society, London, Special Publications 2004, 231, 89-102 (2004)
[9] Belytschko, T.; Black, T., Elastic crack growth in finite elements with minimal remeshing, Int. J. Numer. Methods Eng., 45, 601-620 (1999) · Zbl 0943.74061
[10] Bonet, J.; Wood, R. D., Nonlinear Continuum Mechanics for Finite Element Analysis (1997), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0891.73001
[11] Calvetti, F., Discrete modelling of granular materials and geotechnical problems, European Journal of Environmental and Civil Engineering, 12, 7-8, 951-965 (2008)
[12] Chu, J.; Leong, W. K., Effect of fines on instability behaviour of loose sand, Geotechnique, 52, 10, 751-755 (2002)
[13] Ciantia, M. O.; Arroyo, M.; Calvetti, F.; Gens, A., An approach to enhance efficiency of DEM modelling of soils with crushable grains, Geotechnique, 65, 2, 91-110 (2015)
[14] Ciantia, M. O.; Arroyo, M.; Calvetti, F.; Gens, A., A numerical investigation of the incremental behavior of crushable granular soils, Int. J. Numer. Anal. Methods GeoMech., 40, 1773-1798 (2016)
[15] Cil, M. B.; Sohn, C.; Buscarnera, G., DEM modeling of grain size effect in brittle granular soils, J. Eng. Mech., 146, 3, Article 04019138 pp. (2020)
[16] Cundall, P. A., A discontinuous future for numerical modelling in geomechanics?, Proceedings of the Institute of Civil Engineers Geotechnical Engineering, 149, 41-47 (2001)
[17] Cundall, P. A.; Strack, O. D.L., The development of constitutive laws for soils using distinct element method, (Proceedings Of the 3^rdNumerical Methods In Geomechanics (1979), Aachen: Aachen Germany)
[18] Daouadji, A.; AlGali, H.; Darve, F.; Zeghloul, A., Instability in granular materials: experimental evidence of diffuse mode of failure for loose sands, J. Eng. Mech., 136, 5, 575-588 (2010)
[19] Darve, F.; Servant, G.; Laouafa, F.; Khoa, H. D.V., Failure in geomaterials: continuous and discrete analyses, Comput. Methods Appl. Mech. Eng., 193, 3057-3085 (2004) · Zbl 1067.74565
[20] Delennen, J.-Y.; El Youssoufi, M. S.; Cherblanc, F.; Bénet, J.-C., Mechanical behaviour and failure of cohesive granular materials, Int. J. Numer. Anal. Methods GeoMech., 28, 1577-1594 (2004) · Zbl 1090.74545
[21] di Prisco, C.; Imposimato, S., Experimental analysis and theoretical interpretation of triaxial load controlled loose sand specimen collapses, Mech. Cohesive-Frict. Mater., 2, 93-120 (1997)
[22] Elmekati, A.; El Shamy, U., A practical co-simulation approach for multiscale analysis of geotechnical systems, Comput. Geotech., 37, 494-503 (2010)
[23] Engelder, T.; Peacock, D. C., Joint development normal to regional compression during flexural-flow folding: the Lilstock Buttress Anticline, Somerset, England, J. Struct. Geol., 23, 259-277 (2001)
[24] Fairhurst, C., On the validity of the ‘Brazilian’ test for brittle material, Int. J. Rock Mech. Min. Sci., 1, 535-546 (1964)
[25] Frantík, P.; Veselý, V.; Keršner, Z., Parallelization of lattice modelling for estimation of fracture process zone extent in cementitious composites, Adv. Eng. Software, 60-61, 48-57 (2013)
[26] François, B.; Keita, O., A microstructurally-based internal length for strain localization problems in dynamics, Eur. J. Mech. Solid., 53, 282-293 (2015) · Zbl 1406.74069
[27] Griffith, A. A., The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. Lond. - Ser. A Contain. Pap. a Math. or Phys. Character, 221, 163-198 (1921)
[28] Gui, Y. L.; Hu, W.; Zhao, Z. Y.; Zhu, X., Numerical modelling of a field soil desiccation test using a cohesive fracture model with Voronoi tessellations, Acta Geotechnica, 13, 87-102 (2018)
[29] Guo, N.; Zhao, J., 3D multiscale modeling of strain localization in granular media, Comput. Geotech., 80, 360-372 (2016)
[30] Guo, N.; Zhao, J., Multiscale insights into classical geomechanics problems, Int. J. Numer. Anal. Methods GeoMech., 40, 367-390 (2016)
[31] Guo, H.; Aziz, N. I.; Schmidt, L. C., Rock fracture-toughness determination by the Brazilian test, Eng. Geol., 33, 177-188 (1993)
[32] Guo, L.; Latham, J.-P.; Xiang, J., Numerical simulation of breakages of concrete armour units using a three-dimensional fracture model in the context of the combined finite-discrete element method, Comput. Struct., 146, 117-142 (2015)
[33] Guo, L.; Xiang, J.; Latham, J.-P.; Izzuddin, B., A numerical investigation of mesh sensitivity for a new three-dimensional fracture model within the combined finite-discrete element method, Eng. Fract. Mech., 151, 70-91 (2016)
[34] Guo, L.; Latham, J.-P.; Xiang, J., A numerical study of fracture spacing and through-going fracture formation in layered rocks, Int. J. Solid Struct., 110-111, 44-57 (2017)
[35] Hammer, P. C.; Marlowe, O. J.; Stroud, A. H., Numerical integration over simplexes and cones, Math. Comput., 10, 130-137 (1956) · Zbl 0070.35404
[36] Han, Z. D.; Atluri, S. N., SGBEM (for cracked local subdomain) - FEM (for uncracked global structure) alternating method for analyzing 3D surface cracks and their fatigue-growth, Comput. Model. Eng. Sci., 3, 6, 699-716 (2002) · Zbl 1151.74425
[37] Hillerborg, A.; Modéer, M.; Petersson, P.-E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement Concr. Res., 6, 773-782 (1976)
[38] Huang, W.; Sun, D.; Sloan, S. W., Analysis of the failure mode and softening behaviour of sands in true triaxial tests, Int. J. Solid Struct., 44, 1423-1437 (2007) · Zbl 1118.74044
[39] Jansari, C.; Natarajan, S.; Beex, L.; Kannan, K., Adaptive smoothed stable extended finite element method for weak discontinuities for finite elasticity, Eur. J. Mech. Solid., 78, 103824 (2019) · Zbl 07126008
[40] Kaneko, K.; Terada, K.; Kyoya, T.; Kishino, Y., Global-local analysis of granular media in quasi-static equilibrium, Int. J. Solid Struct., 40, 4043-4069 (2003) · Zbl 1038.74530
[41] Khoa, H. D.V.; Georgopoulos, I. O.; Darve, F.; Laouafa, F., Diffuse failure in geomaterials: experiments and modelling, Comput. Geotech., 33, 1-14 (2006)
[42] Klein, P. A.; Foulk, J. W.; Chen, E. P.; Wimmer, S. A.; Gao, H. J., Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods, Theor. Appl. Fract. Mech., 37, 99-166 (2001)
[43] Klerck, P. A.; Sellers, E. J.; Owen, D. R.J., Discrete fracture in quasi-brittle materials under compressive and tensile stress states, Comput. Methods Appl. Mech. Eng., 193, 3035-3056 (2004) · Zbl 1067.74561
[44] Knappett, J. A.; Craig, R. F., Craig’s Soil Mechanics (2012), Spon Press
[45] Lade, P. V., Instability, shear banding, and failure in granular materials, Int. J. Solid Struct., 39, 3337-3357 (2002)
[46] Lade, P. V.; Wang, Q., Analysis of shear banding in true triaxial tests on sand, J. Eng. Mech., 127, 8, 762-768 (2001)
[47] Lama, R. D.; Vutukuri, V. S., Handbook on mechanical properties of rocks: testing techniques and results (1978), Trans Tech Publications
[48] Latham, J.-P.; Munjiza, A.; Mindel, J.; Xiang, J.; Guises, R.; Garcia, X., Modelling of massive particulates for breakwater engineering using coupled FEMDEM and CFD, Particuology, 6, 572-583 (2008)
[49] Li, X.; Chu, X.; Feng, Y. T., A discrete particle model and numerical modeling of the failure modes of granular materials, Eng. Comput., 22, 8, 894-920 (2005) · Zbl 1191.74055
[50] Li, X.; Liang, Y.; Duan, Q.; Schrefler, B. A.; Du, Y., A mixed finite element procedure of gradient Cosserat continuum for second-order computational homogenisation of granular materials, Comput. Mech., 54, 1331-1356 (2014) · Zbl 1311.74125
[51] Lobo-Guerrero, S.; Vallejo, L. E., Discrete element method evaluation of granular crushing under direct shear test conditions, J. Geotech. Geoenviron. Eng., 131, 10, 1295-1300 (2005)
[52] Lockner, D. A.; Byerlee, J. D.; Kuksenko, V.; Ponomarev, A.; Sidorin, A., Quasi-static fault growth and shear fracture energy in granite, Nature, 350, 39-42 (1991)
[53] Ma, G.; Zhou, W.; Chang, X.-L.; Chen, M.-X., A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method, Granul. Matter, 18, 7 (2016)
[54] Ma, G.; Chen, Y.; Yao, F.; Zhou, W.; Wang, Q., Evolution of particle size and shape towards a steady state: insights from FDEM simulations of crushable granular materials, Comput. Geotech., 112, 147-158 (2019)
[55] Mahabadi, O. K.; Lisjak, A.; Grasselli, G.; Lukas, T.; Munjiza, A., Numerical modelling of a triaxial test of homogeneous rocks using the combined finite-discrete element method, (Proceedings of the ISRM International Symposium - EUROCK 2010 (2010)), (Lausanne, Switzerland)
[56] Mahabadi, O. K.; Lisjak, A.; Munjiza, A.; Grasselli, G., Y-Geo: new combined finite-discrete element numerical code for geomechanical applications, Int. J. GeoMech., 12, 676-688 (2012)
[57] Mahabadi, O. K.; Randall, N. X.; Zong, Z.; Grasselli, G., A novel approach for micro-scale characterization and modelling of geomaterials incorporating actual material heterogeneity, Geophys. Res. Lett., 39, L01303 (2012)
[58] Mahabadi, O. K.; Tatone, B. S.A.; Grasselli, G., Influence of microscale heterogeneity and microstructure on the tensile behaviour of crystalline rocks, J. Geophys. Res.: Solid Earth, 119, 5324-5341 (2014)
[59] Malekan, M.; Silva, L. L.; Barros, F. B.; Pitangueira, R. L.S.; Penna, S. S., Two-dimensional fracture modeling with the generalized/extended finite element method: an object-oriented programming approach, Adv. Eng. Software, 115, 168-193 (2018)
[60] Martin, C. L.; Bouvard, D.; Shima, S., Study of particle rearrangement during powder compaction by the Discrete Element Method, J. Mech. Phys. Solid., 51, 667-693 (2003) · Zbl 1091.74504
[61] Meng, F.; Thouless, M. D., Cohesive-zone analyses with stochastic effects, illustrated by an example of kinetic crack growth, J. Mech. Phys. Solid., 132, 103686 (2019)
[62] Miehe, C.; Dettmar, J.; Zäh, D., Homogenization and two-scale simulations of granular materials for different microstructural constraints, Int. J. Numer. Methods Eng., 83, 1206-1236 (2010) · Zbl 1197.74084
[63] Monteiro Azevedo, N.; Lemos, J. V., Hybrid discrete element/finite element method for fracture analysis, Comput. Methods Appl. Mech. Eng., 195, 4579-4593 (2006) · Zbl 1123.74049
[64] Morris, J. P.; Rubin, M. B.; Blair, S. C.; Glenn, L. A.; Heuze, F. E., Simulations of underground structures subjected to dynamic loading using the distinct element method, Eng. Comput., 21, 384-408 (2004) · Zbl 1062.74663
[65] Morris, J. P.; Rubin, M. B.; Block, G. I.; Bonner, M. P., Simulations of fracture and fragmentation of geologic materials using combined FEM/DEM analysis, Int. J. Impact Eng., 33, 463-473 (2006)
[66] Munjiza, A., The Combined Finite-Discrete Element Method (2004), Wiley and Sons: Wiley and Sons New York · Zbl 1194.74452
[67] Munjiza, A.; Andrews, K. R.F., NBS contact detection algorithm for bodies of similar size, Int. J. Numer. Methods Eng., 43, 131-149 (1998) · Zbl 0937.74079
[68] Munjiza, A.; Andrews, K. R.F., Penalty function method for combined finite-discrete element systems comprising large number of separate bodies, Int. J. Numer. Methods Eng., 49, 1377-1396 (2000) · Zbl 1010.74067
[69] Munjiza, A.; Andrews, K. R.; White, J. K., Combined single and smeared crack model in combined finite-discrete element analysis, Int. J. Numer. Methods Eng., 44, 41-57 (1999) · Zbl 0936.74071
[70] Nadimi, S.; Fonseca, J., A micro finite-element model for soil behaviour, Geotechnique, 68, 4, 290-302 (2018)
[71] Nelson, R. A., Geological Analysis of Naturally Fractured Reservoirs (2001), Gulf Professional Publishing: Gulf Professional Publishing Houston
[72] Nguyen, T. K.; Combe, G.; Caillerie, D.; Desrues, J., FEM×DEM modelling of cohesive granular materials: numerical homogenisation and multi-scale simulations, Acta Geophys., 62, 5, 1109-1126 (2014)
[73] Nicot, F.; Sibille, L.; Donze, F.; Darve, F., From microscopic to macroscopic second-order work in granular assemblies, Mech. Mater., 39, 664-684 (2007) · Zbl 1196.74055
[74] Nicot, F.; Daouadji, A.; Laouafa, F.; Darve, F., Second-order work, kinetic energy and diffuse failure in granular materials, Granul. Matter, 13, 19-28 (2011)
[75] Obermayr, M.; Dressler, K.; Vrettos, C.; Eberhard, P., A bonded-particle model for cemented sand, Comput. Geotech., 49, 299-313 (2013)
[76] Oliver, J., Modelling strong discontinuities is solid mechanics via strain softening constitutive equations. Part 1: fundamentals, Int. J. Numer. Methods Eng., 39, 3575-3600 (1996) · Zbl 0888.73018
[77] Oñate, E.; Rojek, J., Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems, Comput. Methods Appl. Mech. Eng., 193, 3087-3128 (2004) · Zbl 1079.74646
[78] Ord, A.; Hobbs, B. E., Fracture pattern formation in frictional, cohesive, granular material, Philosophical Transactions of the Royal Society A, 368, 95-118 (2010)
[79] Ortiz, M.; Leroy, Y.; Needleman, A., A finite element method for localised failure analysis, Comput. Methods Appl. Mech. Eng., 61, 189-214 (1987) · Zbl 0597.73105
[80] Owen, D. R.J.; Feng, Y. T., Parallelised finite/discrete element simulation of multi-fracturing solids and discrete systems, Eng. Comput., 18, 557-576 (2001) · Zbl 0987.74071
[81] Paavilainen, J.; Tuhkuri, J.; Polojärvi, A., 2D combined finite-discrete element method to model multi-fracture of beam structures, Eng. Comput., 26, 6, 578-598 (2009)
[82] Peron, H.; Delenne, J. Y.; Laloui, L.; El Youssoufi, M. S., Discrete element modelling of drying shrinkage and cracking of soils, Comput. Geotech., 36, 61-69 (2009)
[83] Popovics, S., Strength and Related Properties of Concrete: a Quantitative Approach (1998), John Wiley & Sons
[84] Price, N. J.; Cosgrove, J. W., Analysis of Geological Structures (1990), Cambridge University Press: Cambridge University Press Cambridge
[85] Radi, K.; Jauffrès, D.; Deville, S.; Martin, C. L., Elasticity and fracture of brick and mortar materials using discrete element simulations, J. Mech. Phys. Solid., 126, 101-116 (2019)
[86] Rougier, E.; Knight, E. E.; Broome, S. T.; Sussman, A. J.; Munjiza, A., Validation of a three-dimensional finite-discrete element method using experimental results of the Split Hopkinson Pressure Bar test, Int. J. Rock Mech. Min. Sci., 70, 101-108 (2014)
[87] Salehani, M. K.; Irani, N.; Nicola, L., Modeling adhesive contacts under mixed-mode loading, J. Mech. Phys. Solid., 130, 320-329 (2019)
[88] Schellekens, J. C.J.; de Borst, R., A non-linear finite element approach for the analysis of mode-I free edge delamination in composites, Int. J. Solid Struct., 30, 9, 1239-1253 (1993) · Zbl 0775.73292
[89] Shi, G.; Goodman, R. E., Two dimensional discontinuous deformation analysis, Int. J. Numer. Anal. Methods GeoMech., 9, 6, 541-556 (1985) · Zbl 0573.73106
[90] Shterenlikht, A.; Margetts, L.; Cebamanos, L., Modelling fracture in heterogeneous materials on HPC systems using a hybrid MPI/Fortran coarray multi-scale CAFE framework, Adv. Eng. Software, 125, 155-166 (2018)
[91] Sibille, L.; Nicot, F.; Donzé, F. V.; Darve, F., Material instability in granular assemblies from fundamentally different models, Int. J. Numer. Anal. Methods GeoMech., 31, 457-481 (2007) · Zbl 1196.74055
[92] Sibille, L.; Donzé, F.-V.; Nicot, F.; Chareyre, B.; Darve, F., From bifurcation to failure in a granular material: a DEM analysis, Acta Geotechnica, 3, 15-24 (2008)
[93] Tu, F.; Ling, D.; Hu, C.; Zhang, R., DEM-FEM analysis of soil failure process via the separate edge coupling method, Int. J. Numer. Anal. Methods GeoMech., 41, 1157-1181 (2017)
[94] Turon, A.; Dávila, C. G.; Camanho, P. P.; Costa, J., An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models, Eng. Fract. Mech., 74, 1665-1682 (2007)
[95] Tvergaard, V., Cohesive zone representations of failure between elastic or rigid solids and ductile solids, Eng. Fract. Mech., 70, 1859-1868 (2003)
[96] Tvergaard, V., Study of localization in a void-sheet under stress states near pure shear, Int. J. Solid Struct., 75-76, 134-142 (2015)
[97] Vardoulakis, I., Shear band inclination and shear modulus of sand in biaxial tests, Int. J. Numer. Anal. Methods GeoMech., 4, 103-119 (1980) · Zbl 0443.73092
[98] Vermeer, P. A., The orientation of shear bands in biaxial tests, Geotechnique, 40, 2, 223-236 (1990)
[99] Vermeer, P. A.; de Borst, R., Non-associated plasticity for soils, concrete and rock, Heron, 29, 3, 3-64 (1984)
[100] Wang, Q.; Lade, P. V., Shear banding in true triaxial tests and its effect on failure in sand, J. Eng. Mech., 127, 8, 754-761 (2001)
[101] Wang, J.; Yan, H., On the role of particle breakage in the shear failure behavior of granular soils by DEM, Int. J. Numer. Anal. Methods GeoMech., 37, 832-854 (2013)
[102] Wu, H.; Pollard, D. D., An experimental study of the relationship between joint spacing and layer thickness, J. Struct. Geol., 17, 6, 887-905 (1995)
[103] Wyart, E.; Duflot, M.; Coulon, D.; Martiny, P.; Pardoen, T.; Remacle, J.-F.; Lani, F., Substructuring FE-XFE approaches applied to three-dimensional crack propagation, J. Comput. Appl. Math., 215, 626-638 (2008) · Zbl 1350.74023
[104] Xian, L., Bicanic, N., Owen, D. R. J., and Munjiza, A. (1991). Rock blasting simulation by rigid body dynamics analysis and rigid brittle fracturing model. In Bicanic N. et al., editors, Proceedings NEC-91, International Conference on Nonlinear Engineering Computations, 577-587, Pineridge Press, Swansea, UK.
[105] Xiang, J.; Munjiza, A.; Latham, J.-P., Finite strain, finite rotation quadratic tetrahedral element for the combined finite-discrete element method, Int. J. Numer. Methods Eng., 79, 946-978 (2009) · Zbl 1171.74453
[106] Yan, B.; Regueiro, R. A.; Sture, S., Three-dimensional ellipsoidal discrete element modelling of granular materials and its coupling with finite element facets, Eng. Comput., 27, 4, 519-550 (2010) · Zbl 1257.74169
[107] Zhao, J.; Guo, N., The interplay between anisotropy and strain localisation in granular soils: a multiscale insight, Geotechnique, 65, 8, 642-656 (2015)
[108] Zoback, M. D., Reservoir Geomechanics (2010), Cambridge University Press: Cambridge University Press New York · Zbl 1189.74005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.