Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
권호 표지

Fracture Simulation of UHPFRC Girder with the Interface Type Model

경계형 모델을 사용한 초고강도 섬유보강 콘크리트거더의 파괴역학적 해석

  • 궈이홍 (금오공과대학교 토목환경공학부 토목공학과) ;
  • 한상묵 (금오공과대학교 토목환경공학부)
  • Received : 2009.09.29
  • Accepted : 2009.11.27
  • Published : 2010.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the fracture simulation of UHPFRC girder with the interface type model. Based on the existing numerical simulation of quasi-brittle fracture in normal strength concrete, constitutive modeling for UHPFRC I-girder has been improved by including a tensile hardening at the failure surface. The finite element formulation is based on a triangular unit, constructed from constant strain triangles, with nodes along its sides and neither at the vertex nor the center of the unit. Fracture is simulated through a hardening/softening fracture constitutive law in tension, a softening fracture constitutive law in shear as well as in compression at the boundary nodes, with the material within the triangular unit remaining linear elastic. LCP is used to formulate the path-dependent hardening-softening behavior in non-holonomic rate form and a mathematical programming algorithm is employed to solve the LCP. The piece-wise linear inelastic yielding-failure/failure surface is modeled with two compressive caps, two Mohr-Coulomb failure surfaces, a tensile yielding surface and a tensile failure surface. The comparison between test results and numerical results indicates this method effectively simulates the deformation and failure of specimen.

본 연구는 선형 상보법으로 초고강도 섬유보강 콘크리트 I형보의 파괴역학적 해석을 수치해석으로 수행하였다. 기존의 보통강도 콘크리트에 대한 유사 취성 파괴역학적 수치해석을 기반으로 초고강도 섬유보강 콘크리트 재료역학적 구성모델파괴 면에 인장경화 관계를 도입함으로써 초고강도 섬유보강 콘크리트 I형 거더 해석을 개선시켰다. 상수변형률 삼각형 요소에 꼭지점 또는 요소의 중앙점 절점을 배제하고 요소의 변에 절점을 배치한 결합된 삼각형 요소를 사용하였다. 인장영역에서는 경화/연화 파괴역학적 구성모델을, 전단영역에서는 연화 파괴역학적 구성모델을, 경계절점의 압축에 대해서는 연화파괴역학적 구성모델을 사용하여 파괴역학적 해석을 수행하였다. Non-holonomic rate 형태로 경로에 의존적인 경화연화거동을 LCP로 방정식을 구성하였으며, 그 해는 PATH를 사용해서 구하였다. Piece-wise 비탄성 항복-파괴면은 두 개의 압축 caps, 두 개의 Mohr-Coulomb 파괴면, 인장항복면과 인장파괴면 등으로 구성하였다. 초고강도 섬유보강 콘크리트 거더의 변형거동과 파괴 상태와 비교하여 이 수치해석 방법에 대한 유효성을 검증하였다.

Keywords

References

  1. Attard, M.M., Tin-Loi F. (1999) Fracture Simulation Using a Discrete Triangular Element, ACMSM 16 Sedney, NSW, Austrilia, pp.11-16.
  2. Attard, M.M., Tin-Loi, F. (2005) Numerical Simulation of Quasi-Brittle Fracture in Concrete, Engineering Fracture Mechanics, 72, pp.387-411. https://doi.org/10.1016/j.engfracmech.2004.03.012
  3. Bolzon, G., Mairer, G., Novati, G. (1994) Some Aspects of Quasi-Brittle Fracture Analysis as a Linear Complementarity Problem, Fracture & Damage in Quasi-Brittle Structure, pp.159-174.
  4. Bolzon, G., Mairer, G., Tin-Loi, F. (1995) Holonomic and Nonholonomic Simulations of Quasi-Brittle Fracture: A Comparative Study of Mathematical Programming an Approach, Fracture Mechanics of Concrete Structures, 2, pp.885-898.
  5. Chaimoon, K. (2007) Numerical Simulation of Fracture in Unreinforced Masonry, Ph.D thesis.
  6. Chaimoon, K., Attard, M.M. (2007) Modeling of Unreinforced Masonry Wall under Shear and Compression, Engineering structures, 29, pp.2056-2068. https://doi.org/10.1016/j.engstruct.2006.10.019
  7. Chote, S., Barzin, M. (2007) Flexural Modeling of Strain Softening and Strain Hardening Fiber Reinforced Concrete, 5th High Performance Fiber Reinforced Cement Composites(HPFRCC5), pp.155-164.
  8. De, B.R. (2002) Fracture in Quasi-Brittle Materials: A Review of Continuum Damage-Based Approaches, Engineering Fracture Mechanics, 69, pp.95-112. https://doi.org/10.1016/S0013-7944(01)00082-0
  9. Dirkes, S.P., Ferris, M.C. (1995) The Path Solver: a Nonmonotone Stabilization Scheme for Mixed Complementarity Problems, Optim. Meht. Software, pp.123-156.
  10. Giovanni, M., Alberto, M. (2007) Strengthening of R/Cbeams with High Performance Fiber Reinforced Cementituious Composites, 5th High Performance Fiber Reinforced Cement Composites, pp.389-397.
  11. Han, S.M., Guo, Y.H. (2009) Nonlinear Finite Element Analysis of UHPFRC I-Beam on the Basic of an Elastic-Plastic Fracture Model, 한국전산구조공학회논문집, 22(3), pp.199-209.
  12. Kittinum, S., Sherif E.T. (2007) Three-Dimensional Plasticity Model for High Performance Fiber Reinforced Cement Composites, 5th High Performance Fiber Reinforced Cement Composites(HPFRCC5), pp.231-240.
  13. Maier, G. (1970) A Matrix Structural Theory of Piecewise-Linear Elastoplsticity with Interaction Yield Planes, Meccanica, 5, pp.54-66. https://doi.org/10.1007/BF02133524
  14. Que, N.S., Tin-Loi, F. (2002) Numerical Evaluation of Cohesive Fracture Parameters from a Wedge Splitting Test, Engineering Fracture Mechanics, 69, pp.1269-1286. https://doi.org/10.1016/S0013-7944(01)00131-X
  15. Tin-Loi, F., Li, H. (2000) Numerical Simulations of Quasi-Brittle Fracture Processes Using the Discrete Cohesive Crack Model, Mechanical Sciences, 42, pp.367-379. https://doi.org/10.1016/S0020-7403(98)00115-5
  16. Tin-Loi, F., Xia, S.H. (2001) Holonomic Softening: Models and Analysis, Sruct. & Mech., 29, pp.65-84.
  17. Wu, X.G. (2008) Flexure and Shear Behavior of Ultra High Performance Concrete Post Tension I Shaped Composite Girder, Ph.D thesis.
  18. Wu, X.G., Han, S.M. (2009) Multiple Cracking Model of Fiber Reinforced High Performance Cementitious Composites under Uniaxial Tension, Concrete Structures and Material, 3(1), pp.71-77. https://doi.org/10.4334/IJCSM.2009.3.1.071