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Drucker-Prager plasticity model in the framework of OSB-PD theory with shear deformation

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Abstract

The Drucker-Prager (D-P) model is a representative elastoplastic model for geomaterials because hydrostatic pressure is considered. This paper proposes an ordinary state-based peridynamic (OSB-PD) model with shear deformation based on D-P model and the associated flow rule to study the plastic and damage behaviors of geomaterials. By considering the second invariant of the stress deviator J2 and the first invariant function of stress tensor I1 as the function of peridynamic energy density, the D-P yield function in nonlocal form can be used in peridynamics. In addition, the equivalent stress and equivalent plastic strain in this PD model with shear deformation are determined. Several examples are used to verify the validity of the proposed PD model. The PD results are compared with those obtained by the finite element method (FEM). It implies that the proposed method is effective and accurate.

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References

  1. Zhang LW, Xie Y, Lyu D, Li S (2019) Multiscale modeling of dislocation patterns and simulation of nanoscale plasticity in body-centered cubic (BCC) single crystals. J Mech Phys Solids 130:297–319. https://doi.org/10.1016/j.jmps.2019.06.006

    Article  MathSciNet  MATH  Google Scholar 

  2. Oberhollenzer S, Tschuchnigg F, Schweiger HF (2018) Finite element analyses of slope stability problems using non-associated plasticity. J Rock Mech Geotech Eng 10:1091–1101. https://doi.org/10.1016/j.jrmge.2018.09.002

    Article  Google Scholar 

  3. Randolph MF, Goh SH, Lee FH, Yi JT (2012) A numerical study of cone penetration in fine-grained soils allowing for consolidation effects. Géotechnique 62:707–719

    Article  Google Scholar 

  4. Liao M, Zhang P (2019) An improved approach for computation of stress intensity factors using the finite element method. Theor Appl Fract Mech 101:185–190. https://doi.org/10.1016/j.tafmec.2019.02.019

    Article  Google Scholar 

  5. Moës N, JohnBelytschko DT (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:13.0.CO;2-J

    Article  MathSciNet  MATH  Google Scholar 

  6. Agathos K, Bordas SPA, Chatzi E (2018) Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization. Comput Methods Appl Mech Eng 346:1051–1073

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen JW, Zhou XP, Berto F (2019) The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method. Fatigue Fract Eng Mater Struct 42:397–414. https://doi.org/10.1111/ffe.12918

    Article  Google Scholar 

  8. Zhou X, Chen J (2019) Extended finite element simulation of step-path brittle failure in rock slopes with non-persistent en-echelon joints. Eng Geol 250:65–88

    Article  Google Scholar 

  9. Schlangen E, Van MJGM (1992) Simple lattice model for numerical simulation of fracture of concrete materials and structures. Mater Struct 25:534–542

    Article  Google Scholar 

  10. Kadau K, Germann TC, Lomdahl PS (2011) Molecular dynamics comes of age: 320 billion atom simulation on BlueGene/L. Int J Mod Phys C 17:1755–1761

    Article  Google Scholar 

  11. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209. https://doi.org/10.1016/S0022-5096(99)00029-0

    Article  MathSciNet  MATH  Google Scholar 

  12. Silling SA, Epton M, Weckner O et al (2007) Peridynamic states and constitutive modeling. J Elast 88:151–184. https://doi.org/10.1007/s10659-007-9125-1

    Article  MathSciNet  MATH  Google Scholar 

  13. Seleson P, Ha YD, Beneddine S (2015) Concurrent coupling of bond-based peridynamics and the navier equation of classical elasticity by blending. Int J Multiscale Comput Eng 13:91–113

    Article  Google Scholar 

  14. Wang L, Abeyaratne R (2018) A one-dimensional peridynamic model of defect propagation and its relation to certain other continuum models. J Mech Phys Solids 116:334–349

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang Y, Zhou X, Wang Y, Shou Y (2018) A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids. Int J Solids Struct 134:89–115. https://doi.org/10.1016/j.ijsolstr.2017.10.022

    Article  Google Scholar 

  16. Beckmann R, Mella R, Wenman MR (2013) Mesh and timestep sensitivity of fracture from thermal strains using peridynamics implemented in Abaqus. Comput Methods Appl Mech Eng 263:71–80

    Article  MathSciNet  MATH  Google Scholar 

  17. Le QV, Bobaru F (2018) Surface corrections for peridynamic models in elasticity and fracture. Comput Mech 61:499–518. https://doi.org/10.1007/s00466-017-1469-1

    Article  MathSciNet  MATH  Google Scholar 

  18. Lai X, Liu L, Li S et al (2018) A non-ordinary state-based peridynamics modeling of fractures in quasi-brittle materials. Int J Impact Eng 111:130–146

    Article  Google Scholar 

  19. Yaghoobi A, Chorzepa MG (2017) Fracture analysis of fiber reinforced concrete structures in the micropolar peridynamic analysis framework. Eng Fract Mech 169:238–250. https://doi.org/10.1016/j.engfracmech.2016.11.004

    Article  Google Scholar 

  20. Silling SA (2017) Stability of peridynamic correspondence material models and their particle discretizations. Comput Methods Appl Mech Eng 322:42–57

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang LJ, Xu JF, Wang JX (2019) Elastodynamics of linearized isotropic state-based peridynamic media. J Elast 137:157–176

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhu F, Zhao J (2019) A peridynamic investigation on crushing of sand particles. Geotechnique 69:526–540. https://doi.org/10.1680/jgeot.17.P.274

    Article  Google Scholar 

  23. Liu S, Fang G, Liang J et al (2020) A new type of peridynamics: element-based peridynamics. Comput Methods Appl Mech Eng 366:113098. https://doi.org/10.1016/j.cma.2020.113098

    Article  MathSciNet  MATH  Google Scholar 

  24. Fang G, Liu S, Fu M et al (2019) A method to couple state-based peridynamics and finite element method for crack propagation problem. Mech Res Commun 95:89–95

    Article  Google Scholar 

  25. Wang Y, Zhou X, Zhang T (2019) Size effect of thermal shock crack patterns in ceramics: Insights from a nonlocal numerical approach. Mech Mater 137:103133. https://doi.org/10.1016/j.mechmat.2019.103133

    Article  Google Scholar 

  26. Zhu QZ, Ni T (2017) Peridynamic formulations enriched with bond rotation effects. Int J Eng Sci 121:118–129. https://doi.org/10.1016/j.ijengsci.2017.09.004

    Article  MathSciNet  MATH  Google Scholar 

  27. Wang Y, Zhou X, Kou M (2018) Numerical studies on thermal shock crack branching instability in brittle solids. Eng Fract Mech 204:157–184. https://doi.org/10.1016/j.engfracmech.2018.08.028

    Article  Google Scholar 

  28. Mitchell JA (2011) A nonlocal, ordinary, state-based plasticity model for peridynamics. United States. https://doi.org/10.2172/1018475

    Article  Google Scholar 

  29. Lammi CJ, Vogler TJ (2014) A nonlocal peridynamic plasticity model for the dynamic flow and fracture of concrete. Sandia National Lab.(SNL-CA), Livermore, CA. United States.

  30. Madenci E, Oterkus S (2016) Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening. J Mech Phys Solids 86:192–219. https://doi.org/10.1016/j.jmps.2015.09.016

    Article  MathSciNet  Google Scholar 

  31. Pashazad H, Kharazi M (2019) A peridynamic plastic model based on von Mises criteria with isotropic, kinematic and mixed hardenings under cyclic loading. Int J Mech Sci 156:182–204. https://doi.org/10.1016/j.ijmecsci.2019.03.033

    Article  Google Scholar 

  32. Liu ZM, Bie YH, Cui ZQ, Cui XY (2020) Ordinary state-based peridynamics for nonlinear hardening plastic materials’ deformation and its fracture process. Eng Fract Mech 223:106782. https://doi.org/10.1016/j.engfracmech.2019.106782

    Article  Google Scholar 

  33. Madenci E (2017) Peridynamic integrals for strain invariants of homogeneous deformation. ZAMM-Zeitschrift fur Angew Math und Mech 97:1236–1251. https://doi.org/10.1002/zamm.201600242

    Article  MathSciNet  Google Scholar 

  34. Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer, Berlin

    Book  MATH  Google Scholar 

  35. Ren H, Zhuang X, Rabczuk T (2016) A new peridynamic formulation with shear deformation for elastic solid. J Micromech Mol Phys 01:1650009. https://doi.org/10.1142/s2424913016500090

    Article  Google Scholar 

  36. Drucker DC (1959) A definition of stable inelastic material. Trans ASME J Appl Mech 26:101–106

    Article  MathSciNet  MATH  Google Scholar 

  37. Foster J, Silling SA, Chen WN (2011) An energy based failure criterion for use with peridynamic states. Int J Multiscale Comput Eng 9:675–688. https://doi.org/10.1615/intjmultcompeng.2011002407

    Article  Google Scholar 

  38. Shen F, Zhang Q, Huang D (2013) Damage and failure process of concrete structure under uniaxial compression based on Peridynamics modeling. Math Probl Eng 2013:631074. https://doi.org/10.1155/2013/631074

    Article  Google Scholar 

  39. Zhang Y, Qiao P (2018) An axisymmetric ordinary state-based peridynamic model for linear elastic solids. Comput Methods Appl Mech Eng 341:517–550. https://doi.org/10.1016/j.cma.2018.07.009

    Article  MathSciNet  MATH  Google Scholar 

  40. Zhang T, Zhou XP (2019) A modified axisymmetric ordinary state-based peridynamics with shear deformation for elastic and fracture problems in brittle solids. Eur J Mech A/Solids 77:103810. https://doi.org/10.1016/j.euromechsol.2019.103810

    Article  MathSciNet  MATH  Google Scholar 

  41. Kilic B, Madenci E (2010) An adaptive dynamic relaxation method for quasi-static simulation using the peridynamic theory. Theor Appl Fract Mech 53:194–204

    Article  Google Scholar 

Download references

Acknowledgements

The work is supported by the National Natural Science Foundation of China (Nos. 51839009, 51679017) and the Graduate Scientific Research and Innovation Foundation of Chongqing, China (Grant No. CYB20033).

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Authors and Affiliations

  1. School of Civil Engineering, Chongqing University, Chongqing, 400045, People’s Republic of China

    Ting Zhang & Xiao-Ping Zhou

  2. PLA University of Science and Technology, Nanjing, 210014, Jiangsu, People’s Republic of China

    Qi-Hu Qian

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  1. Ting Zhang
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Correspondence to Xiao-Ping Zhou.

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Zhang, T., Zhou, XP. & Qian, QH. Drucker-Prager plasticity model in the framework of OSB-PD theory with shear deformation. Engineering with Computers 39, 1395–1414 (2023). https://doi.org/10.1007/s00366-021-01527-z

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