Elasto-Plasticity of Granular Micro-Structures

미소구조에서의 탄소성모델

  • 박재균 (단국대학교 토목환경공학과)
  • Published : 2005.12.01

Abstract

This study deals with elasto-plasticity of granular micro-structures which recovers continuum elasto-plasticity in its counterpart. The theory is based on doublet mechanics that assumes particles of finite size and connecting linear springs, and it makes extensions to plasticity. The result shows that the micro model has one to one relationship with the continuum model in the simplest case. Micro-strain and micro-stress of two dimensional plane stress problem were calculated, which shows the behavior of the specimen and verifies the effectiveness of this model.

본 논문은 연속체역학에서의 탄소성모델을 그대로 재현할 수 있는 미소구조모델에 관해서 연구하였다. 물체를 일정크기를 지닌 입자와 그 입자들을 연결하는 선형 스프링으로 모델링한 Doublet Mechanics를 기본이론으로 하여 이를 소성 영역으로 확장하였다. 그 결과로 가장 단순한 가정을 하였을 경우 미소모델과 연속체모델이 정확히 일대일 대응을 하는 것을 보였다. 2차원 평면응력문제에 대한 예제를 통해 미소변형률과 미소응력을 계산하였고 그 결과로 거동에 대해 분석하여 이 모델의 유효성을 입증하였다.

Keywords

References

  1. 이홍우, 조진래 (2005) 페트로프-갤러킨 자연요소법 : I. 개념, 한국전산구조공학회논문집, 18(2), pp.103-112
  2. 이홍우, 조진래 (2005) 페트로프-갤러킨 자연요소법 : II. 선형 정탄성 해석, 한국전산구조공학회논문집, 18(2), pp.113-121
  3. 이홍우, 조진래 (2005) 페트로프-갤러킨 자연요소법 : III. 기하학적 비선형 해석, 한국전산구조공학회논문집, 18(2), pp.123-131
  4. 大田孝二(2000) 교량과 강재, 구미서관(번역판)
  5. Belvtschko , T., Lu , Y.Y., Gu , L.(1994) Elementfree Galerkin methods. International Journal for Numerical Methods in Engineering, 37, pp.229-256 https://doi.org/10.1002/nme.1620370205
  6. Chang, C.S., Gao, J.(1995) Second-gradient constitutive theory for granular material with random packing structure, International Journal of Solids and Structures, 32(16), pp.2279-2293 https://doi.org/10.1016/0020-7683(94)00259-Y
  7. Eringen, A.C.(1968) Theory of micro-polar elasticity, Liebowiz, H. (Ed.). Fracture-An advanced Treatise, vol. II. Academic Press, pp.621-693
  8. Ferrari, M., Granik, V.T., Iman, A., Nadeau, J.C. (1997) Advances in doublet mechanics, Springer
  9. Granik, V.T., Ferrari, M. (1993) Microstructural mechanics of granular media, Mechanics of Materials, 15, pp.301-322 https://doi.org/10.1016/0167-6636(93)90005-C
  10. Gurtin, M.E.(2000) On the plasticity of single crystal: free energy. microforces, plastic-strain gradients, Journal of Mechanics and Physics of Solids, 48, pp.989-1036 https://doi.org/10.1016/S0022-5096(99)00059-9
  11. Maddalena, F., Ferrari, M. (1995) Viscoelasticity of granular materials, Mechanics of Materials, 20, pp.241-250 https://doi.org/10.1016/0167-6636(94)00064-6
  12. Pietruszczak, S., Mroz, Z. (2000) Formulation of anisotropic failure criteria incorporating a microstructure tensor, Computers and Geotechnics, 26, pp, 105-112 https://doi.org/10.1016/S0266-352X(99)00034-8
  13. Sadd , M.H., Dai , Q. (2005) A comparison of micro-mechanical modeling of asphalt materials using finite elements and doublet mechanics, Mechanics of Materials, 37, pp.641-662 https://doi.org/10.1016/j.mechmat.2004.06.004
  14. Simo, J.C., Hughes, T.J.R. (1998) Computational Inelasticity, Springer
  15. Stein, E., de Borst, R., Hughes, T.J.R. (2004) Encyclopedia of Computational Mechanics-Fundamentals, 1, Wiley
  16. Zohdi, T.I., Hutter, K., Wriggers, P. (1999) A technique to describe the macroscopic pressure dependence of diffusive properties of solid materials containing heterogeneities, Computational Materials Science, 15, pp.69-88 https://doi.org/10.1016/S0927-0256(99)00010-5