Advertisement

Acta Mechanica

, Volume 230, Issue 7, pp 2425–2446 | Cite as

Effect of tangential plasticity on structural response under non-proportional cyclic loading

  • S. TsutsumiEmail author
  • R. Fincato
  • H. Momii
Original Paper
  • 21 Downloads

Abstract

In an attempt to correct the unrealistic material stiffness predicted by elastoplastic models which adopt an associative flow rule, this paper introduces an innovative technique for the computation of the inelastic contributions generated in a non-proportional loading path. The formulation of these inelastic contributions takes into account the plastic response along the direction normal to the plastic potential, neglecting the irreversible stretch caused by the tangential component of the stress rate. Here, the introduction of tangential plasticity, in combination with the return mapping technique, eliminates this drawback, allowing fast and accurate computation. The present paper focuses on the evaluation of the load-carrying capacity of a steel bridge pier, indicating the necessity of considering the additional tangential plasticity term for a correct description of the structural response.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Hashiguchi, K., Tsutsumi, S.: Elastoplastic constitutive equation with tangential stress rate effect. Int. J. Plast. 17, 117–145 (2001).  https://doi.org/10.1016/S0749-6419(00)00021-8 CrossRefzbMATHGoogle Scholar
  2. 2.
    Tomita, Y., Shindo, A., Kim, Y.S., Michiura, K.: Deformation behaviour of elastic–plastic tubes under external pressure and axial load. Int. J. Mech. Sci. 28, 263–274 (1986).  https://doi.org/10.1016/0020-7403(86)90040-8 CrossRefzbMATHGoogle Scholar
  3. 3.
    Goya, M., Ito, K.: An expression of elastic–plastic constitutive law incorporating vertex formation and kinematic hardening. J. Appl. Mech. 58, 617 (1991).  https://doi.org/10.1115/1.2897240 CrossRefGoogle Scholar
  4. 4.
    Goya, M., Miyagi, K., Ito, K., Sueyoshi, T., Itomura, S.: Comparison between numerical and analytical predictions of shear localization of sheets subjected to biaxial tension. In: Computational Mechanics ’95, pp. 1396–1401. Springer, Berlin (1995)Google Scholar
  5. 5.
    Hashiguchi, K., Protasov, A.: Localized necking analysis by the subloading surface model with tangential-strain rate and anisotropy. Int. J. Plast. 20, 1909–1930 (2004).  https://doi.org/10.1016/j.ijplas.2003.11.018 CrossRefzbMATHGoogle Scholar
  6. 6.
    Khojastehpour, M., Murakami, Y., Hashiguchi, K.: Antisymmetric bifurcation in an elastoplastic cylinder with tangential plasticity. Mech. Mater. 38, 1061–1071 (2006).  https://doi.org/10.1016/j.mechmat.2005.08.004 CrossRefGoogle Scholar
  7. 7.
    Khojastehpour, M., Hashiguchi, K.: Plane strain bifurcation analysis of soils by the tangential-subloading surface model. Int. J. Solids Struct. 41, 5541–5563 (2004).  https://doi.org/10.1016/j.ijsolstr.2004.04.017 CrossRefzbMATHGoogle Scholar
  8. 8.
    Khojastehpour, M., Hashiguchi, K.: Axisymmetric bifurcation analysis in soils by the tangential-subloading surface model. J. Mech. Phys. Solids. 52, 2235–2262 (2004).  https://doi.org/10.1016/j.jmps.2004.04.005 CrossRefzbMATHGoogle Scholar
  9. 9.
    Tsutsumi, S., Kaneko, K.: Constitutive response of idealized granular media under the principal stress axes rotation. Int. J. Plast. 24, 1967–1989 (2008)CrossRefzbMATHGoogle Scholar
  10. 10.
    Tsutsumi, S., Hashiguchi, K.: General non-proportional loading behavior of soils. Int. J. Plast. 21, 1941–1969 (2005).  https://doi.org/10.1016/j.ijplas.2005.01.001 CrossRefzbMATHGoogle Scholar
  11. 11.
    Fincato, R., Tsutsumi, S.: A return mapping algorithm for elastoplastic and ductile damage constitutive equations using the subloading surface method. Int. J. Numer. Methods Eng. 113, 1729–1754 (2017).  https://doi.org/10.1002/nme.5718 MathSciNetCrossRefGoogle Scholar
  12. 12.
    Fincato, R., Tsutsumi, S.: Closest-point projection method for the extended subloading surface model. Acta Mech. 228(12), 4213–4233 (2017).  https://doi.org/10.1007/s00707-017-1926-0 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Hashiguchi, K.: Elastoplasticity Theory. Springer, Berlin (2009)CrossRefzbMATHGoogle Scholar
  14. 14.
    Yamakawa, Y., Hashiguchi, K., Ikeda, K.: Implicit stress-update algorithm for isotropic Cam-clay model based on the subloading surface concept at finite strains. Int. J. Plast. 26, 634–658 (2010).  https://doi.org/10.1016/j.ijplas.2009.09.007 CrossRefzbMATHGoogle Scholar
  15. 15.
    Tsutsumi, S., Fincato, R.: Cyclic plasticity model for fatigue with softening behaviour below macroscopic yielding. Mater. Des. 165, 107573 (2018).  https://doi.org/10.1016/j.matdes.2018.107573 CrossRefGoogle Scholar
  16. 16.
    Van Do, V.N., Lee, C.H., Chang, K.H.: A nonlinear CDM model for ductile failure analysis of steel bridge columns under cyclic loading. Comput. Mech. 53, 1209–1222 (2014).  https://doi.org/10.1007/s00466-013-0964-2 MathSciNetGoogle Scholar
  17. 17.
    Mróz, Z.: On the description of anisotropic workhardening. J. Mech. Phys. Solids. 15, 163–175 (1967).  https://doi.org/10.1016/0022-5096(67)90030-0 CrossRefGoogle Scholar
  18. 18.
    Mróz, Z., Norris, V.A., Zienkiewicz, O.C.: An anisotropic, critical state model for soils subject to cyclic loading. Géotechnique 31, 451–469 (1981).  https://doi.org/10.1680/geot.1981.31.4.451 CrossRefGoogle Scholar
  19. 19.
    Dafalias, Y.F., Popov, E.P.: A model of nonlinearly hardening materials for complex loading. Acta Mech. 21, 173–192 (1975).  https://doi.org/10.1007/BF01181053 CrossRefzbMATHGoogle Scholar
  20. 20.
    Chaboche, J.L., Dang Van, K., Cordier, G.: Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. Berlin, Germany (1979)Google Scholar
  21. 21.
    Hashiguchi, K.: Subloading surface model in unconventional plasticity. Int. J. Solids Struct. 25, 917–945 (1989).  https://doi.org/10.1016/0020-7683(89)90038-3 CrossRefzbMATHGoogle Scholar
  22. 22.
    Dafalias, Y.F.: Corotational rates for kinematic hardening at large plastic deformations. J. Appl. Mech. 50, 561 (1983).  https://doi.org/10.1115/1.3167091 CrossRefzbMATHGoogle Scholar
  23. 23.
    Xiao, H., Bruhns, O.T., Meyers, A.: Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mech. 124, 89–105 (1997).  https://doi.org/10.1007/BF01213020 MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Rudnicki, J.W., Rice, J.R.: Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids. 23, 371–394 (1975).  https://doi.org/10.1016/0022-5096(75)90001-0 CrossRefGoogle Scholar
  25. 25.
    Tsutsumi, S., Momii, H., Fincato, R.: Tangential plasticity effect on buckling behavior of a thin wall pier under cyclic loading condition. Q. J. Jpn. Weld. Soc. 33, 161s–165s (2015).  https://doi.org/10.2207/qjjws.33.161s CrossRefGoogle Scholar
  26. 26.
    Chaboche, J.L.: Time-independent constitutive theories for cyclic plasticity. Int. J. Plast. 2, 149–188 (1986).  https://doi.org/10.1016/0749-6419(86)90010-0 CrossRefzbMATHGoogle Scholar
  27. 27.
    Wilkins, M.L.: Calculation of Elastic–Plastic Flow. Academic Press, New York (1964)Google Scholar
  28. 28.
    Krieg, R.D., Krieg, D.B.: Accuracies of numerical solution methods for the elastic-perfectly plastic model. J. Press. Vessel Technol. 99, 510 (1977).  https://doi.org/10.1115/1.3454568 CrossRefGoogle Scholar
  29. 29.
    Simo, J.C., Ortiz, M.: A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Comput. Methods Appl. Mech. Eng. 49, 221–245 (1985).  https://doi.org/10.1016/0045-7825(85)90061-1 CrossRefzbMATHGoogle Scholar
  30. 30.
    Pillinger, I., Hartley, P., Sturgess, C.E.N., Rowe, G.W.: Use of a mean-normal technique for efficient and numerically stable large-strain elastic–plastic finite-element solutions. Int. J. Mech. Sci. 28, 23–29 (1986).  https://doi.org/10.1016/0020-7403(86)90004-4 CrossRefzbMATHGoogle Scholar
  31. 31.
    Hughes, T.J.R., Pister, K.S.: Consistent linearization in mechanics of solids and structures. Comput. Struct. 8, 391–397 (1978).  https://doi.org/10.1016/0045-7949(78)90183-9 MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Huang, J., Griffiths, D.V.: Return mapping algorithms and stress predictors for failure analysis in geomechanics. J. Eng. Mech. 135, 276–284 (2009).  https://doi.org/10.1061/(ASCE)0733-9399(2009)135:4(276) CrossRefGoogle Scholar
  33. 33.
    de Souza Neto, E.A., Peric, D., Owen, D.R.J.: Computational Methods for Plasticity: Theory and Applications. Wiley (2008)Google Scholar
  34. 34.
    Starman, B., Halilovič, M., Vrh, M., Štok, B.: Consistent tangent operator for cutting-plane algorithm of elasto-plasticity. Comput. Methods Appl. Mech. Eng. 272, 214–232 (2014).  https://doi.org/10.1016/j.cma.2013.12.012 MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Miehe, C.: Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity. Comput. Methods Appl. Mech. Eng. 134, 223–240 (1996).  https://doi.org/10.1016/0045-7825(96)01019-5 MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Hashiguchi, K., Suzuki, N., Ueno, M.: Elastoplastic deformation analysis by return-mapping and consistent tangent modulus tensor based on subloading surface model (1st report, formulation of return-mapping). Trans. JSME 80, SMM0083–SMM0083 (2014).  https://doi.org/10.1299/transjsme.2014smm0083. (in Japanese)Google Scholar
  37. 37.
    Fincato, R., Tsutsumi, S.: A numerical study of the return mapping application for the subloading surface model. Eng. Comput. 35, 1314–1343 (2018).  https://doi.org/10.1108/EC-12-2016-0446 CrossRefGoogle Scholar
  38. 38.
    Bonora, N.: A nonlinear CDM model for ductile failure. Eng. Fract. Mech. 58, 11–28 (1997).  https://doi.org/10.1016/S0013-7944(97)00074-X CrossRefGoogle Scholar
  39. 39.
    Tai, W.H., Yang, B.X.: A new microvoid-damage model for ductile fracture. Eng. Fract. Mech. 25, 377–384 (1986).  https://doi.org/10.1016/0013-7944(86)90133-5 CrossRefGoogle Scholar
  40. 40.
    Nishikawa, K., Yamamoto, S., Natori, T., Terao, K., Yasunami, H., Terada, M.: Retrofitting for seismic upgrading of steel bridge columns. Eng. Struct. 20, 540–551 (1998).  https://doi.org/10.1016/S0141-0296(97)00025-4 CrossRefGoogle Scholar
  41. 41.
    Yu, H.S., Yuan, X.: On a class of non-coaxial plasticity models for granular soils. Proc. R. Soc. A Math. Phys. Eng. Sci 462, 725–748 (2006).  https://doi.org/10.1098/rspa.2005.1590 CrossRefzbMATHGoogle Scholar
  42. 42.
    Hashiguci, K.: Generalized subloading surface model with tangential stress rate effect. J. Appl. Mech. 8, 507–518 (2005).  https://doi.org/10.2208/journalam.8.507 CrossRefGoogle Scholar
  43. 43.
    Roscoe, K.H.: The influence of strains in soil mechanics. Géotechnique 20, 129–170 (1970).  https://doi.org/10.1680/geot.1970.20.2.129 CrossRefGoogle Scholar
  44. 44.
    Goto, Y., Kumar, G.P., Kawanishi, N.: Nonlinear finite-element analysis for hysteretic behavior of thin-walled circular steel columns with in-filled concrete. J. Struct. Eng. 136, 1413–1422 (2010).  https://doi.org/10.1061/(ASCE)ST.1943-541X.0000240 CrossRefGoogle Scholar
  45. 45.
    Goto, Y., Wang, Q., Obata, M.: FEM analysis for hysteretic behavior of thin-walled columns. J. Struct. Eng. 124, 1290–1301 (1998).  https://doi.org/10.1061/(ASCE)0733-9445(1998)124:11(1290) CrossRefGoogle Scholar
  46. 46.
    Gao, S., Usami, T., Ge, H.: Ductility evaluation of steel bridge piers with pipe sections. J. Eng. Mech. 124, 260–267 (1998).  https://doi.org/10.1061/(ASCE)0733-9399(1998)124:3(260) CrossRefGoogle Scholar
  47. 47.
    Ucak, A., Tsopelas, P.: Load path effects in circular steel columns under bidirectional lateral cyclic loading. J. Struct. Eng. 141, 04014133 (2015).  https://doi.org/10.1061/(ASCE)ST.1943-541X.0001057 CrossRefGoogle Scholar
  48. 48.
    Tsutsumi, S., Toyosada, M., Hashiguchi, K.: Extended subloading surface model incorporating elastic boundary concept. J. Appl. Mech. 9, 455–462 (2006).  https://doi.org/10.2208/journalam.9.455 CrossRefGoogle Scholar
  49. 49.
    Suzuki, Y., Ono, K., Ikeuchi, T., Okada, S., Nishimura, N., Takahashi, M.: Development of constitutive equation for construction steel. In: Proceedings of the 6th Symposium on Ductility Design Method for Bridges, pp. 351–358 (in Japanese) (2003)Google Scholar
  50. 50.
    Hu, F., Shi, G., Shi, Y.: Constitutive model for full-range elasto-plastic behavior of structural steels with yield plateau: formulation and implementation. Eng. Struct. 171, 1059–1070 (2018).  https://doi.org/10.1016/j.engstruct.2016.02.037 CrossRefGoogle Scholar
  51. 51.
    Fujimoto, M., Hashimoto, A., Nakagomi, T., Yamada, T.: Study on fracture of welded connections in steel structures under cyclic loads based on nonlinear fracture mechanism: part 1 formulation of multi-axial stress–strain relations of structural steel for cyclic loads. J. Struct. Constr. Eng. (Trans. AIJ) 356, 93–102 (1985).  https://doi.org/10.3130/aijsx.356.0_93 CrossRefGoogle Scholar
  52. 52.
    Fincato, R., Tsutsumi, S., Momii, H.: Evaluation of the horizontal load-carrying capacity of a thin steel bridge pier by means of the damage subloading surface model. MATEC Web Conf. 165, 22013 (2018).  https://doi.org/10.1051/matecconf/201816522013 CrossRefGoogle Scholar
  53. 53.
    Fincato, R., Tsutsumi, S.: Numerical modeling of the evolution of ductile damage under proportional and non-proportional loading. Int. J. Solids Struct. (2018).  https://doi.org/10.1016/j.ijsolstr.2018.10.028 Google Scholar
  54. 54.
    Ucak, A., Tsopelas, P.: Accurate modeling of the cyclic response of structural components constructed of steel with yield plateau. Eng. Struct. 35, 272–280 (2012).  https://doi.org/10.1016/j.engstruct.2011.10.015 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Joining and Welding Research InstituteOsaka UniversityIbarakiJapan
  2. 2.Nikken Engineering CorporationNogataJapan

Personalised recommendations