To utilize the geometry smoothness of isogeometric analysis for solid media and the effectiveness of the discrete element method for particulate matters, a coupled three-dimensional isogeometric/discrete element method is developed to model the contact interaction between structures and particles. The coupling procedure for handling interactions between isogeometric elements and discrete elements includes global search, local search/resolution and interaction force calculation. Since interaction models for contacting particles and isogeometric elements have significant effects on the contact forces in simulations, several commonly used contact models, including linear, Hertz and quadratic models, are investigated. For a small ball impacting a thick plate example, it is found that the Hertz contact model exhibits the best behavior as the interaction law between a sphere and an isogeometric element in the elastic regime, and no additional correction factor is needed. In addition, an assembly of randomly arranged granular particles impacting a tailor rolled blank is also simulated to further illustrate the applicability of the proposed method.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65
Munjiza AA, Knight EE, Rougier E (2011) Computational mechanics of discontinua. Wiley, New York
Gao W, Liu L, Liao Z, Chen S, Zang M, Tan Y (2019a) Discrete element analysis of the particle mixing performance in a ribbon mixer with a double u-shaped vessel. Granul Matter 21(1):12. https://doi.org/10.1007/s10035-018-0864-4
Han K, Peric D, Owen D, Yu J (2000) A combined finite/discrete element simulation of shot peening processes-part II: 3D interaction laws. Eng Comput 17(6):680–702
Munjiza AA (2004) The combined finite-discrete element method. Wiley, London
Owen D, Feng Y, de Souza Neto E, Cottrell M, Wang F, Andrade Pires F et al (2004) The modelling of multi-fracturing solids and particulate media. Int J Numer Methods Eng 60(1):317–339
Onate E, Rojek J (2004) Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems. Comput Methods Appl Mech Eng 193(27–29):3087–3128
Xiang J, Munjiza A, Latham JP (2009) Finite strain, finite rotation quadratic tetrahedral element for the combined finite-discrete element method. Int J Numer Methods Eng 79(8):946–978
Zang M, Gao W, Lei Z (2011) A contact algorithm for 3D discrete and finite element contact problems based on penalty function method. Comput Mech 48(5):541–550
Gao W, Tan Y, Jiang S, Zhang G, Zang M (2016) A virtual-surface contact algorithm for the interaction between FE and spherical DE. Finite Elem Anal Des 108:32–40
Zheng Z, Zang M, Chen S, Zeng H (2018) A GPU-based DEM–FEM computational framework for tire-sand interaction simulations. Comput Struct 209:74–92
Munjiza A, Knight EE, Rougier E (2015) Large strain finite element method: a practical course. Wiley, New York
Dang HK, Meguid MA (2013) An efficient finite-discrete element method for quasi-static nonlinear soil-structure interaction problems. Int J Numer Anal Methods Geomech 37(2):130–149
Tran V, Meguid M, Chouinard L (2013) A finite-discrete element framework for the 3D modeling of geogrid-soil interaction under pullout loading conditions. Geotext Geomembr 37:1–9
Hu L, Hu G, Fang Z, Zhang Y (2013) A new algorithm for contact detection between spherical particle and triangulated mesh boundary in discrete element method simulations. Int J Numer Methods Eng 94(8):787–804
Chen H, Zhang Y, Zang M, Hazell PJ (2015) An accurate and robust contact detection algorithm for particle-solid interaction in combined finite-discrete element analysis. Int J Numer Methods Eng 103(8):598–624
Gao W, Zang M (2014) The simulation of laminated glass beam impact problem by developing fracture model of spherical DEM. Eng Anal Bound Elem 42:2–7
Wriggers P (2006) Computational contact mechanics, 2nd edn. Springer, Berlin
Santasusana M (2017) Numerical techniques for non-linear analysis of structures combining discrete element and finite element methods. Ph.D. thesis, Polytechnic University of Catalonia
Feng Y, Owen D (2004) A 2D polygon/polygon contact model: algorithmic aspects. Eng Comput 21(2/3/4):265–277
Feng YT, Han K, Owen DRJ (2012) Energy-conserving contact interaction models for arbitrarily shaped discrete elements. Comput Methods Appl Mech Eng 205–208:169–177
Hughes TJ, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39–41):4135–4195
Cottrell JA, Hughes TJ, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, New York
Gao W, Wang J, Yin S, Feng Y (2019b) A coupled 3D isogeometric and discrete element approach for modelling interactions between structures and granular matters. Comput Methods Appl Mech Eng 354:441–463
Cox MG (1972) The numerical evaluation of b-splines. IMA J Appl Math 10(2):134–149
De Boor C (1972) On calculating with b-splines. J Approx Theory 6(1):50–62
Temizer I, Wriggers P, Hughes T (2011) Contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 200(9–12):1100–1112
Di Renzo A, Di Maio FP (2004) Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem Eng Sci 59(3):525–541
Escotet-Espinoza MS, Foster CJ, Ierapetritou M (2018) Discrete element modeling (DEM) for mixing of cohesive solids in rotating cylinders. Powder Technol 335:124–136
Johnson KL, Johnson KL (1987) Contact mechanics. Cambridge University Press, Cambridge
Williams JR, Perkins E, Cook B (2004) A contact algorithm for partitioning n arbitrary sized objects. Eng Comput 21(2/3/4):235–248
De Lorenzis L, Wriggers P, Zavarise G (2012) A mortar formulation for 3d large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method. Comput Mech 49(1):1–20
Kim JY, Youn SK (2012) Isogeometric contact analysis using mortar method. Int J Numer Methods Eng 89(12):1559–1581
De Lorenzis L, Wriggers P, Hughes TJ (2014) Isogeometric contact: a review. GAMM-Mitteilungen 37(1):85–123
De Lorenzis L, Temizer I, Wriggers P, Zavarise G (2011) A large deformation frictional contact formulation using NURBS-based isogeometric analysis. Int J Numer Methods Eng 87(13):1278–1300
Dimitri R, De Lorenzis L, Scott M, Wriggers P, Taylor R, Zavarise G (2014) Isogeometric large deformation frictionless contact using T-splines. Comput Methods Appl Mech Eng 269:394–414
Matzen M, Cichosz T, Bischoff M (2013) A point to segment contact formulation for isogeometric, NURBS based finite elements. Comput Methods Appl Mech Eng 255:27–39
Moré JJ, Cosnard MY (1979) Numerical solution of nonlinear equations. ACM Trans Math Softw 5(1):64–85
Brent RP (1973) Some efficient algorithms for solving systems of nonlinear equations. SIAM J Numer Anal 10(2):327–344
Kopačka J, Gabriel D, Plešek J, Ulbin M (2016) Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems. Int J Numer Methods Eng 105(11):803–833
Spendley W, Hext GR, Himsworth FR (1962) Sequential application of simplex designs in optimisation and evolutionary operation. Technometrics 4(4):441–461
Zheng Z, Zang M, Chen S, Zhao C (2017) An improved 3D DEM–FEM contact detection algorithm for the interaction simulations between particles and structures. Powder Technol 305:308–322
Reed J (1985) Energy losses due to elastic wave propagation during an elastic impact. J Phys D Appl Phys 18(12):2329
McLaskey GC, Glaser SD (2010) Hertzian impact: experimental study of the force pulse and resulting stress waves. J Acoust Soc Am 128(3):1087–1096
This work is supported by NNSF of China (Grant Nos. 51878184 and 51404209). The support is greatly acknowledged.
Conflict of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Gao, W., Feng, Y.T. A coupled 3D discrete elements/isogeometric method for particle/structure interaction problems. Comp. Part. Mech. 7, 869–880 (2020). https://doi.org/10.1007/s40571-019-00267-8
- Isogeometric analysis
- Discrete element
- Contact interaction model