State of the Art of the Cyclic Plasticity Models of Structural Steel

구조용 강재의 반복소성모델 분석 연구

  • 이은택 (중앙대학교 공과대학 건축학과)
  • Received : 2002.09.17
  • Published : 2002.12.27

Abstract

The task of plastic theory is twofold: first, to set up relationships between stress and strain that adequately describe the observed plastic deformation of metals, and second, to develop techniques for using these relationships in studying of the mechanics of metal forming processes, and the anlaysis and design of structures. One of the major problems in the theory of plasticity is to describe the behavior of work-hardening materials in the plastic range for complex loading histories. This can be achieved by formulating constitutive laws either in the integral or differential forms. To adequately predict the response of steel members during cyclic loading, the hardening rule must account for the features of cyclic stress-strain behavior. Neithe of the basic isotropic and kinematic hardening rules is suitable for describing cyclic streess-strain behavior, although a kinematic hardening rule describes the nearly linear portions of the stabilized hystersis loops. There is also a limited expansion of the yield surface as predicted by the isotropic hardening rule. Strong ground motions or wind gusts affect the complex and nonproportional loading histories in the inelastic behavior of structues rather than the proportional loading. Nonproportional loading is defined as externally applied forces on the structure, with variable ratios during the entire loading history. This also includes the rate of time-dependency of the loads. For nonproportional loading histories, unloading may take place along a chord instead of the radius of the load surface. In such cases, the shape of the stress-strain curve has to be determined experimentally for all non-radial loading conditions. The plasticity models including two surface models ae surveyed based on a yield surface and a bound surface that represent a state of maximum stress. This paper is concerned with the improvement of a plasticity models of the two-surface type for structural steel. This is follwed by an overview of plasticity models on structural steel. Finally the need for further research is identified.

소성이론이의 연구방향은 일반적으로 두 가지 대별된다. 첫 째는 강재의 소성변형을 적절하게 나타내는 응력-변형도 관계를 정립하는 것이고, 둘 째는 위의 과정을 이용한 기법을 개발하고 구조물을 설계하는 것이다. 소성이론을 연구하는데 한 가지 중요한 문제는 복잡한 하중이력에 대하여 소성영역에서 경화재료의 거동을 묘사하는 것이다. 또한 구조물이 강한 지진이나 바람하중을 받을 경우, 비례하중보다는 복잡한 불비례하중에 의하여 영향을 받는다. 따라서 소성이론과 강재의 소성거동에 대한 연구는 불비례하중의 거동과 영향을 나타낼 수 있어야 한다. 지금까지 많은 연구자들이 이 분야에서 이론을 발표하였고, 지금도 계속하여 새로운 소성모델 연구를 하고 있다. 본 논문은 지금까지 가장 많이 쓰이고 있는 소성 모델을 two-surface 소성모델을 중심으로 분석하고 각 소성모델의 특징과 문제점을 파악하였고 앞으로의 연구과제를 제안하였다.

Keywords

Acknowledgement

Supported by : 중앙대학교

References

  1. 강구조 이론과 한계상태설계 김덕재;이은택
  2. Acta Mechanica v.1 A Rule of Anisotropic Hardening Baltov, A.;Sawczuk, A.
  3. Journal of Applied Mechanics v.25 A Theory of Elastic, Plastic and Creep Deformation of an Initially Isotropic Material Showing Strain Hardening, Creep Recovery, and Secondary Creep Besseling, J. F.
  4. Plasticity for Engineers Calladine, C. R.
  5. Journal of the Engineering Mechanics v.112 no.8 Constitutive Reations of Structural Steel Under Nonproportional Loading Chang, K. C.;Lee, G. C.
  6. Plasticity for Structural Engineers Chen, W. F.;Han, D. J.
  7. Dissertation presented to Stanford University in 1983, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Cyclic Stress-Strain and Moment-Curvature Relationships for Steel Beams and Columns Cofie, N. G.
  8. Acta Mechanica v.21 no.3 A Model for Nonlinearly Hardening Materials for Complex Loading Dafalias, Y. F.;Popov, E. P.
  9. Journal of Applied Mechanics v.98 no.4 Plastic Internal Variables Formalism of Cyclic Plasticity Dafalias, Y. F.;Popov, E. P.
  10. Physical Review v.47 no.6 On the Plasticity of Crystals Duwez, P.
  11. Acta Mechanica v.15 On Nonlinear Kinematic Hardening Eisenberg, M. A.LPhillips, A.
  12. Journal of the Structrual Division v.107 no.ST1 Inelastic Material Models in Earthquake Response Hays, C. O. Jr.
  13. Journal of the Structural Division v.105 no.ST7 Inelastic Section Response by Tangent Stiffness Hays, C. O. Jr.;Santhanam, T. K.
  14. The Mathematical Theory of Plasticity Hill, R.
  15. IUTAM Colloquium Madrid The Theory of Piecewise Linear Isotropic Plasticity Hodge, P. G. Jr.
  16. Journal of Applied Mechanics v.23 Discussion of [Prager, W., "A New Method of Analyzing Stresses and Strains in Work-Hardening Plastic Solids"] Hodge, P. G. Jr.
  17. Journal of Applied Mechanics, Trans. ASME. v.34 On a Class of Models for the Yielding Behavior of Continuous and Composite Systems Iwan, W. D.
  18. Applied Mathematics and Mechanics v.22 The Theory of Plasticity Which Takes Into Account Residual Microstresses Kadashevich, I. I.;Novozhilov, V. V.
  19. Journal of Engineering Mechanics v.114 no.4 Plasticity Theory Based on Fuzzy Sets Klisinski, M.
  20. Journal of Basic Engineering v.93D Cyclic Plasticity -Some Properties of the Hysteresis Curve of Structural Metals at Room Temperature Krempl. E.
  21. Journal of Applied Mechanics v.97 A Practical Two Surface Plasticity Theory Krieg, R. D.
  22. Journal of Engineering Materials and Technology, Transactions of the ASME, January v.100 Cyclic Plasticity for Nonproportional Paths Cyclic Hardening Lamba, H. S.;Sidebottom, O. M.
  23. Journal of Engineering Materials and Technology, Transsactions of the ASME, January v.100 Cyclic Plasticity for Nonproportional Paths: Comparison with Predictions of Three Incremental Plasticity Models Lamba, H. S.;Sidebottom;O. M.
  24. Journal of Engineering Mechanics v.127 no.9 Bounding Surface Model for Geosynthetic Reinforcements Ling, H. I.;Lin, H.;Mohri, Y.;Kawabata, T.
  25. Introduction to the Mechanics of a Continuous Medium Malvern, L. E.
  26. Journal of Applied Mechanics v.52 A Two Surface Model for Transient Nonproportional Cyclic Plasticity: Development of Appropriate Equations McDowell, D. L.
  27. Journal of Applied Mechanics v.52 A Two Surface Model for Transient Nonproportional Cyclic Plasticity: Comparison of Theory with Experiments McDowell, D. L.
  28. Journal ofEngineering Materials and Technology v.107 An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity McDowell, D. L.
  29. Journal of Applied Mechanics v.54 An Evaluation of Recent Development in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity McDowell, D. L.
  30. In IABSE Symposium on the Resistance and ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads Method of Analysis for Cyclically Loaded Reinforced Concrete Plan Frames Including Changes in Geometry and Nonelastic Behavior of Eleements under Combined Normal Force and Bending Menegotto, M.;Pinto, P.
  31. Stability and Ductility of Steel Structures under Cyclic Loading A Uniaxial Stress-Strain Model for Structural Steels under Cyclic Loading Mizuno, E.;Shen, C.;Tanaka, Y.;Usami, T.;Fukumoto, Y.(ed.);Lee, G. C.(ed.)
  32. J. Mech. Phys. Solid v.15 On the Description of Anisotropic Work Hardening Mroz, Z.
  33. Acta Mechanica v.7 An Attempt to Describe the Behaviour of Metals Under Cyclic Loads Using a More General Workhardening Model Mroz, Z.
  34. International Journal of Solids and Structures v.15 Yield Surfaces and Loading Surfaces. Experiments and Recommendations Phillips, A.;Lee, C. W.
  35. Acta Mechanica v.14 An Experimental Investigation of yield Surfaces at Elevated Temperatures Phillips, A.;Liu, C. S.;Justussons, J. W.
  36. Acta Mechanica v.27 An Experimental Investigation Concerning Yield Surfaces and Loading Surfaces Phillips, A.;Moon, H.
  37. Acta Mechanica v.1 On the Concept of the Yield Surface Phillips, A.;Sierakowski, R. L.
  38. International Journal of Solids and Structures v.8 The Effect of Loading Path on the Yield Surface at Elevated Temperatures Phillips, A.;Tang, J. L.
  39. Acta Mechanica v.20 Some New Observations on Yield Surfaces Phillips, A.;Tang, J. L.;Ricciuti, M.
  40. Journal of the Engineering Mechanics Division v.104 no.EM6 Cyclic Metal Plasticity: Experiments and Theory Popov, E. P.;Petersson, H.
  41. Journal of Applied Mechanics v.78 A New Method of Analyzing Stresses and Strains in Work-Hardening Plastic Solids Prager, W.
  42. NACA, TN No. 902. 1943 Description of Stress-Strain Curves by Three Parameters Ramberg, W.;Osgood, W. R.
  43. Nuclear Engineering and Design v.29 On Nonlinear Kinematic Hardening Plasticity Theory Rashid, Y. R.
  44. Journal of the Structural Division v.105 no.ST1 Model for Mild Steel in Inelastic Frame Analysis Santhanam, T. K.
  45. Journal of Engineering Mechanics v.121 no.11 Cyclic Behavior of Structural Steels. II: Theory Shen, C.;Mamaghani, I. H. P.;Mizuno, E.;Usami, T.
  46. Journal of Engineering Mechanics v.113 no.12 Endochronic Theory for Structural Steel Under Nonproportional Loading Sugiura, K.;Lee, G. C.;Chang, K. C.
  47. Journal of the Engineering Mechanics v.109 no.3 Simple Plasticity Model of Two-Surface Type Tseng, N. T.;Lee, G. C.
  48. Acta Mechanica v.81 A Generalized Eulerian Two-Surface Cyclic Plasticity Model for Finite Strains Voyiadjis, G. Z.;Kattan, P. I.
  49. Journal of Engineering Mechanics v.21 no.1 Inelastic Behavior of Steel Members under Nonproportional Loading Yang, C. F.;Lee, Eun Taik;Chang, K. C.;Lee, G. C.
  50. Quarterly of Applied Mathematics v.17 no.1 A Modification of Prager's Hardening Rule Ziegler, H.