DEM–FEM simulation of tire–sand interaction based on improved contact model

  • Peng Yang
  • Mengyan ZangEmail author
  • Haiyang Zeng


In the interaction between rubber tire and granular terrain, the dynamic behavior of granular terrain is significantly affected not only by the shape of soil grains, but also by the deformation contact of tread rubber. Therefore, the effect of these two factors should be considered in tire–sand interactions. In this study, an improved contact model including the effect of sand grain shape and tread rubber deformation is developed for dealing with the interaction between rubber tire and sand terrain. In sand–sand contact model, the interaction between sand grains takes the form of surface contact instead of conventional point contact, where the contact calculation contains four interactions, i.e., normal force, tangential force, rolling resistance and twisting resistance. And in tread–sand contact model, the contact between tread rubber and sand grains is surface contact, which includes the rolling resistance and twisting resistance on the grains caused by rubber deformation during contact. As a result, the complete and realistic evaluation of contact forces is accomplished. Next, a comparison of sandpile simulation of coarse particles and experiment is carried out to verify the effectiveness of the sand–sand contact model. Finally, the novel contact model is applied to tire–sand interaction simulations and compared with the single-wheel experiments. The results indicate that the proposed contact model can be a powerful tool to simulate the interactions between rubber tire and sand terrain.


DEM–FEM Rubber tire Sand terrain Contact model Grain shape Rubber deformation 



This work was supported by the National Key R&D Program of China (No. 2017YFE0117300), the Science and Technology Planning Project of Guangzhou (No. 201804020065), the National Natural Science Foundation of China (No. 11672344).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.


  1. 1.
    El-Sayegh Z, El-Gindy M, Johansson I et al (2018) Improved tire–soil interaction model using FEA-SPH simulation. J Terrramech 78:53–62CrossRefGoogle Scholar
  2. 2.
    Cueto OG, Coronel CEI, Morfa CAR et al (2013) Three dimensional finite element model of soil compaction caused by agricultural tire traffic. Comput Electron Agric 99:146–152CrossRefGoogle Scholar
  3. 3.
    Xia K (2011) Finite element modeling of tire/terrain interaction: application to predicting soil compaction and tire mobility. J Terrramech 48(2):113–123CrossRefGoogle Scholar
  4. 4.
    Hernandez JA, Al-Qadi IL (2016) Semicoupled modeling of interaction between deformable tires and pavements. J Transp Eng Part A Syst 143(4):04016015CrossRefGoogle Scholar
  5. 5.
    Li H, Schindler C (2013) Analysis of soil compaction and tire mobility with finite element method. Proc Inst Mech Eng Part K J Multi-body Dyn 227(3):275–291CrossRefGoogle Scholar
  6. 6.
    Rubinstein D, Shmulevich I, Frenckel N (2018) Use of explicit finite-element formulation to predict the rolling radius and slip of an agricultural tire during travel over loose soil. J Terrramech 80:1–9CrossRefGoogle Scholar
  7. 7.
    Yamashita H, Jayakumar P, Alsaleh M et al (2018) Physics-based deformable tire–soil interaction model for off-road mobility simulation and experimental validation. J Comput Nonlinear Dyn 13(2):021002CrossRefGoogle Scholar
  8. 8.
    Ozaki S, Kondo W (2016) Finite element analysis of tire traveling performance using anisotropic frictional interaction model. J Terrramech 64:1–9CrossRefGoogle Scholar
  9. 9.
    Behnke R, Wollny I, Hartung F et al (2019) Thermo-mechanical finite element prediction of the structural long-term response of asphalt pavements subjected to periodic traffic load: tire–pavement interaction and rutting. Comput Struct 218:9–31CrossRefGoogle Scholar
  10. 10.
    Smith W, Peng H (2013) Modeling of wheel–soil interaction over rough terrain using the discrete element method. J Terrramech 50(5–6):277–287CrossRefGoogle Scholar
  11. 11.
    Du Y, Gao J, Jiang L et al (2017) Numerical analysis of lug effects on tractive performance of off-road wheel by DEM. J Braz Soc Mech Sci Eng 39(6):1977–1987CrossRefGoogle Scholar
  12. 12.
    Du Y, Gao J, Jiang L et al (2018) Development and numerical validation of an improved prediction model for wheel–soil interaction under multiple operating conditions. J Terrramech 79:1–21CrossRefGoogle Scholar
  13. 13.
    Jiang M, Dai Y, Cui L et al (2018) Experimental and DEM analyses on wheel–soil interaction. J Terrramech 76:15–28CrossRefGoogle Scholar
  14. 14.
    Nakashima H, Takatsu Y, Shinone H et al (2009) FE-DEM analysis of the effect of tread pattern on the tractive performance of tires operating on sand. J Mech Syst Transp Logist 2(1):55–65CrossRefGoogle Scholar
  15. 15.
    Nishiyama K, Nakashima H, Yoshida T et al (2016) 2D FE–DEM analysis of tractive performance of an elastic wheel for planetary rovers. J Terrramech 64:23–35CrossRefGoogle Scholar
  16. 16.
    Nishiyama K, Nakashima H, Shimizu H et al (2017) 2D FE–DEM analysis of contact stress and tractive performance of a tire driven on dry sand. J Terrramech 74:25–33CrossRefGoogle Scholar
  17. 17.
    Nishiyama K, Nakashima H, Yoshida T et al (2018) FE–DEM with interchangeable modeling for off-road tire traction analysis. J Terrramech 78:15–25CrossRefGoogle Scholar
  18. 18.
    Michael M, Vogel F, Peters B (2015) DEM–FEM coupling simulations of the interactions between a tire tread and granular terrain. Comput Methods Appl Mech Eng 289:227–248MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Horner DA, Peters JF, Carrillo A (2001) Large scale discrete element modeling of vehicle–soil interaction. J Eng Mech 127(10):1027–1032CrossRefGoogle Scholar
  20. 20.
    Recuero A, Serban R, Peterson B et al (2017) A high-fidelity approach for vehicle mobility simulation: nonlinear finite element tires operating on granular material. J Terrramech 72:39–54CrossRefGoogle Scholar
  21. 21.
    Yamashita H, Chen G, Ruan Y et al (2019) Hierarchical multiscale modeling of tire–soil interaction for off-road mobility simulation. J Comput Nonlinear Dyn 14(6):061007CrossRefGoogle Scholar
  22. 22.
    Zhao C, Zang M (2014) Analysis of rigid tire traction performance on a sandy soil by 3D finite element–discrete element method. J Terrramech 55(7):29–37CrossRefGoogle Scholar
  23. 23.
    Zhao CL, Zang MY (2017) Application of the FEM/DEM and alternately moving road method to the simulation of tire–sand interactions. J Terrramech 72:27–38CrossRefGoogle Scholar
  24. 24.
    Zhao C, Zang M, Chen S et al (2018) Improving the 3D finite–discrete element method and its application in the simulation of wheel–sand interactions. Int J Comput Methods 15(07):1850059MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Zheng Z, Zang M, Chen S et al (2018) A GPU-based DEM–FEM computational framework for tire–sand interaction simulations. Comput Struct 209:74–92CrossRefGoogle Scholar
  26. 26.
    Zeng H, Xu W, Zang M et al (2019) Experimental and numerical investigations of tractive performance of off-road tires on gravel terrain. Int J Comput Methods. CrossRefGoogle Scholar
  27. 27.
    Nassauer B, Liedke T, Kuna M (2013) Polyhedral particles for the discrete element method. Granul Matter 15(1):85–93CrossRefGoogle Scholar
  28. 28.
    Eliáš J (2014) Simulation of railway ballast using crushable polyhedral particles. Powder Technol 264:458–465CrossRefGoogle Scholar
  29. 29.
    Govender N, Wilke DN, Wu CY et al (2018) Large-scale GPU based DEM modeling of mixing using irregularly shaped particles. Adv Powder Technol 29(10):2476–2490CrossRefGoogle Scholar
  30. 30.
    Khazeni A, Mansourpour Z (2018) Influence of non-spherical shape approximation on DEM simulation accuracy by multi-sphere method. Powder Technol 332:265–278CrossRefGoogle Scholar
  31. 31.
    Xu T, Yu J, Yu Y et al (2018) A modelling and verification approach for soybean seed particles using the discrete element method. Adv Powder Technol 29(12):3274–3290CrossRefGoogle Scholar
  32. 32.
    He Y, Evans TJ, Shen YS et al (2018) Discrete modelling of the compaction of non-spherical particles using a multi-sphere approach. Miner Eng 117:108–116CrossRefGoogle Scholar
  33. 33.
    Iwashita K, Oda M (2000) Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol 109(1–3):192–205CrossRefGoogle Scholar
  34. 34.
    Jiang MJ, Yu HS, Harris D (2005) A novel discrete model for granular material incorporating rolling resistance. Comput Geotech 32(5):340–357CrossRefGoogle Scholar
  35. 35.
    Jiang M, Shen Z, Wang J (2015) A novel three-dimensional contact model for granulates incorporating rolling and twisting resistances. Comput Geotech 65:147–163CrossRefGoogle Scholar
  36. 36.
    Horabik J, Molenda M (2016) Parameters and contact models for DEM simulations of agricultural granular materials: a review. Biosyst Eng 147:206–225CrossRefGoogle Scholar
  37. 37.
    Markauskas D, Kačianauskas R (2011) Investigation of rice grain flow by multi-sphere particle model with rolling resistance. Granul Matter 13(2):143–148CrossRefGoogle Scholar
  38. 38.
    Ai J, Chen JF, Rotter JM et al (2011) Assessment of rolling resistance models in discrete element simulations. Powder Technol 206(3):269–282CrossRefGoogle Scholar
  39. 39.
    Wakui F, Terumichi Y (2011) Numerical simulation of tire–ground system considering soft ground characteristics. J Syst Des Dyn 5(8):1650–1661Google Scholar
  40. 40.
    Matsushima T (2005) Effect of irregular grain shape on quasi-static shear behavior of granular assembly. Powders Grains 2:1319–1323Google Scholar
  41. 41.
    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  42. 42.
    Balevičius R, Džiugys A, Kačianauskas R (2004) Discrete element method and its application to the analysis of penetration into granular media. J Civ Eng Manag 10(1):3–14CrossRefGoogle Scholar
  43. 43.
    Perez JCL, Kwok CY, Senetakis K (2016) Effect of rubber size on the behaviour of sand–rubber mixtures: a numerical investigation. Comput Geotech 80:199–214CrossRefGoogle Scholar
  44. 44.
    Tekeste MZ, Balvanz LR, Hatfield JL et al (2019) Discrete element modeling of cultivator sweep-to-soil interaction: worn and hardened edges effects on soil–tool forces and soil flow. J Terrramech 82:1–11CrossRefGoogle Scholar
  45. 45.
    Luding S (2008) Cohesive, frictional powders: contact models for tension. Granul Matter 10(4):235MathSciNetzbMATHCrossRefGoogle Scholar
  46. 46.
    Gardiner BS, Tordesillas A (2006) Effects of particle size distribution in a three-dimensional micropolar continuum model of granular media. Powder Technol 161(2):110–121CrossRefGoogle Scholar
  47. 47.
    Huang J, da Silva MV, Krabbenhoft K (2013) Three-dimensional granular contact dynamics with rolling resistance. Comput Geotech 49:289–298CrossRefGoogle Scholar
  48. 48.
    Lei Z, Zang M (2010) An approach to combining 3D discrete and finite element methods based on penalty function method. Comput Mech 46(4):609–619MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    Zang MY, Lei Z, Wang SF (2007) Investigation of impact fracture behavior of automobile laminated glass by 3D discrete element method. Comput Mech 41(1):73–83zbMATHCrossRefGoogle Scholar
  50. 50.
    Li Y, Xu Y, Thornton C (2005) A comparison of discrete element simulations and experiments for ‘sandpiles’ composed of spherical particles. Powder Technol 160(3):219–228CrossRefGoogle Scholar
  51. 51.
    Derakhshani SM, Schott DL, Lodewijks G (2015) Micro-macro properties of quartz sand: experimental investigation and DEM simulation. Powder Technol 269:127–138CrossRefGoogle Scholar
  52. 52.
    Dai L, Sorkin V, Vastola G et al (2019) Dynamics calibration of particle sandpile packing characteristics via discrete element method. Powder Technol 347:220–226CrossRefGoogle Scholar
  53. 53.
    Ani OA, Uzoejinwa BB, Ezeama AO et al (2018) Overview of soil–machine interaction studies in soil bins. Soil Tillage Res 175:13–27CrossRefGoogle Scholar
  54. 54.
    Hallquist JO (2007) LS-DYNA keyword user’s manual, vol 970. Livermore Software Technology Corporation, California, pp 299–800Google Scholar
  55. 55.
    Syed Z, Tekeste M, White D (2017) A coupled sliding and rolling friction model for DEM calibration. J Terrramech 72:9–20CrossRefGoogle Scholar
  56. 56.
    Zhuang J (2002) Computational vehicle terramechanics. Press of Mechanical Industry, Beijing (in Chinese) Google Scholar
  57. 57.
    Hambleton JP, Drescher A (2009) Modeling wheel-induced rutting in soils: indentation. J Terrramech 46(2):35–47CrossRefGoogle Scholar

Copyright information

© OWZ 2019

Authors and Affiliations

  1. 1.School of Mechanical and Automotive EngineeringSouth China University of TechnologyGuangzhouPeople’s Republic of China

Personalised recommendations